The instructions on Cloudflare's website are confusing and incomplete.
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Install cloudflared: brew install cloudflare/cloudflare/cloudflared
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Create the configuration file: mkdir /usr/local/etc/cloudflared/ && vim /usr/local/etc/cloudflared/config.yml
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With the contents: proxy-dns: true proxy-dns-upstream: - https://1.1.1.1/dns-query - https://1.0.0.1/dns-query
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Enable on system boot: sudo cloudflared service install
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Start the service: sudo launchctl start com.cloudflare.cloudflared
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Test with dig: dig @127.0.0.1 google.com A
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Change your dns settings to point to 127.0.0.1:sudo networksetup -setdnsservers Wi-Fi 127.0.0.1