Still crude, but enough to get the picture...

DiscoveryController.java

import lombok.Getter;
import lombok.RequiredArgsConstructor;
import org.springframework.context.ApplicationContext;
import org.springframework.web.bind.annotation.RequestMapping;
import org.springframework.web.bind.annotation.RequestMethod;
import org.springframework.web.bind.annotation.RestController;
import org.springframework.web.method.HandlerMethod;
import org.springframework.web.servlet.mvc.method.RequestMappingInfo;
import org.springframework.web.servlet.mvc.method.annotation.RequestMappingHandlerMapping;

import javax.annotation.PostConstruct;
import javax.inject.Inject;
import java.util.*;

@RestController
@RequestMapping("/api")
public class DiscoveryController {

    @Inject
    private ApplicationContext ctx;

    private Map<String, MappingInformation> results = new HashMap<String, MappingInformation>();

    @Inject
    private List<RequestMappingHandlerMapping> mappings;

    @PostConstruct
    protected void init(){
        Map<String, RequestMappingHandlerMapping> mappings = ctx.getBeansOfType(RequestMappingHandlerMapping.class);
        for(RequestMappingHandlerMapping mapping : mappings.values()){
            Map<RequestMappingInfo, HandlerMethod> methods = mapping.getHandlerMethods();
            for(RequestMappingInfo info : methods.keySet() ){
                MappingInformation result = get(info.getPatternsCondition().getPatterns().iterator().next());
                result.getMethods().addAll( info.getMethodsCondition().getMethods() );
            }
        }
    }

    private MappingInformation get(String path){
        MappingInformation info = results.get(path);
        if( info == null ){
            info = new MappingInformation(path);
            results.put(path, info);
        }
        return info;
    };

    @RequestMapping("")
    public Collection<MappingInformation> get() throws Exception {
        return results.values();
    }

    @RequiredArgsConstructor
    @Getter
    public static class MappingInformation{
        private final String paths;
        private final Set<RequestMethod> methods = new HashSet<RequestMethod>();
    }
}