https://apoorv.blog/http-api-cloudfront-cdk/

alias.ts

new ARecord(this, 'apiAliasRecord', {
  zone: hostedZone,
  target: RecordTarget.fromAlias(new ApiGatewayv2Domain(domain))
})

certificate.ts

const hostedZone = HostedZone.fromHostedZoneAttributes(this, 'hostedZoneWithAttributes', {
  hostedZoneId,
  zoneName: website_domain
})

const apiCert = new DnsValidatedCertificate(this, 'ApiSSL', {
  domainName: api_domain,
  hostedZone
})

existing-api.ts

const existingAPI = HttpApi.fromHttpApiAttributes(this, 'existingAPI', {
  apiEndpoint: api_domain,
  httpApiId: 'myApiId'
})

http-api.ts

const domain = new DomainName(this, 'api_domain', {
  domainName: api_domain,
  certificate: apiCert
})

const api = new HttpApi(this, 'apiEndpoint', {
  defaultDomainMapping: {
    domainName: domain
  },
  corsPreflight: {
    allowCredentials: true,
    allowHeaders: ['Content-Type'],
    allowMethods: [HttpMethod.GET, HttpMethod.POST, HttpMethod.PUT, HttpMethod.DELETE],
    allowOrigins: [
      'https://example.com'
    ]
  },
  apiName: 'exampleAPI',
  disableExecuteApiEndpoint: true
})

new CfnOutput(this, 'apiID', {
  value: api.httpApiId
})

main-part1.ts

///////////////////////////////
// Part 1
const hostedZone = HostedZone.fromHostedZoneAttributes(this, 'hostedZoneWithAttributes', {
    hostedZoneId,
    zoneName: website_domain
})

const certificate = new DnsValidatedCertificate(this, 'ApiSSL', {
    domainName: website_domain,
    hostedZone
})

const api = new HttpApi(this, 'apiEndpoint', {
    apiName: 'exampleAPISameDomain',
})

new CfnOutput(this, 'apiID', {
    value: api.apiEndpoint
})

const signUpFn = new Function(this, 'signUpFn', {
    runtime: Runtime.NODEJS_14_X,
    code: Code.fromAsset(`${__dirname}/../lambda-fns/sign-up/deployment.zip`),
    handler: 'index.handler',
    memorySize: 512
})
///////////////////////////////

main-part2.ts

///////////////////////////////
// Part 2
api.addRoutes({
    path: '/api/sign-up',
    methods: [HttpMethod.POST],
    integration: new LambdaProxyIntegration({ handler: signUpFn })
})

const apiOriginPolicy = new OriginRequestPolicy(this, 'apiOriginPolicy', {
    cookieBehavior: OriginRequestCookieBehavior.all(),
    headerBehavior: OriginRequestHeaderBehavior.none(),
    queryStringBehavior: OriginRequestQueryStringBehavior.all()
})

const distribution = new Distribution(this, 'websiteAndAPIDistribution', {
    defaultBehavior: {
        origin: new HttpOrigin('origin-source-code.com'),
    },
    additionalBehaviors: {
        'api/*': {
            origin: new HttpOrigin(api.apiEndpoint.replace('https://', '')),
            allowedMethods: AllowedMethods.ALLOW_ALL,
            cachePolicy: CachePolicy.CACHING_DISABLED,
            compress: false,
            originRequestPolicy: apiOriginPolicy,
            viewerProtocolPolicy: ViewerProtocolPolicy.REDIRECT_TO_HTTPS
        }
    },
    domainNames: [website_domain],
    certificate,
    minimumProtocolVersion: SecurityPolicyProtocol.TLS_V1_2_2019,
    enableIpv6: true,
    enabled: true,
    httpVersion: HttpVersion.HTTP2,
    priceClass: PriceClass.PRICE_CLASS_ALL
})
///////////////////////////////

main-part3.ts

///////////////////////////////
// Part 3
new ARecord(this, 'AliasForCloudfront', {
    target: RecordTarget.fromAlias(new CloudFrontTarget(distribution)),
    zone: hostedZone,
    recordName: website_domain
})
///////////////////////////////

route.ts

const signUpFn = new Function(this, 'signUpFn', {
  runtime: Runtime.NODEJS_14_X,
  code: Code.fromAsset(`${__dirname}/../lambda-fns/sign-up/deployment.zip`),
  handler: 'index.handler',
  memorySize: 512
})

api.addRoutes({
  path: '/sign-up',
  methods: [HttpMethod.POST],
  integration: new LambdaProxyIntegration({ handler: signUpFn })
})

sub-part1.ts

///////////////////////////////
// Part 1
const hostedZone = HostedZone.fromHostedZoneAttributes(this, 'hostedZoneWithAttributes', {
  hostedZoneId,
  zoneName: website_domain
})

const apiCert = new DnsValidatedCertificate(this, 'ApiSSL', {
  domainName: api_domain,
  hostedZone
})
///////////////////////////////

sub-part2.ts

///////////////////////////////
// Part 2
const domain = new DomainName(this, 'api_domain', {
  domainName: api_domain,
  certificate: apiCert
})

const api = new HttpApi(this, 'apiEndpoint', {
  defaultDomainMapping: {
    domainName: domain
  },
  corsPreflight: {
    allowCredentials: true,
    allowHeaders: ['Content-Type'],
    allowMethods: [HttpMethod.GET, HttpMethod.POST, HttpMethod.PUT, HttpMethod.DELETE],
    allowOrigins: [
      'https://example.com'
    ]
  },
  apiName: 'exampleAPI',
  disableExecuteApiEndpoint: true
})

new CfnOutput(this, 'apiID', {
  value: api.httpApiId
})

const signUpFn = new Function(this, 'signUpFn', {
  runtime: Runtime.NODEJS_14_X,
  code: Code.fromAsset(`${__dirname}/../lambda-fns/sign-up/deployment.zip`),
  handler: 'index.handler',
  memorySize: 512
})
///////////////////////////////

sub-part3.ts

///////////////////////////////
// Part 3
new ARecord(this, 'apiAliasRecord', {
  zone: hostedZone,
  target: RecordTarget.fromAlias(new ApiGatewayv2Domain(domain))
})

api.addRoutes({
  path: '/sign-up',
  methods: [HttpMethod.POST],
  integration: new LambdaProxyIntegration({ handler: signUpFn })
})
///////////////////////////////