I have noticed there are two options for method-level throttling in the apigateway.RestApi.

1. You can add methodOptions when creating the gateway, but this doesn’t actually work, as the changes never sync up to the AWS UI console (as an ‘override’ for the method within the Stage).

2. You can also alter the Usage Plan under throttling to specify fine-grained methods, but you must also activate the coarse-grained (whole of API) throttling too.

See https://docs.aws.amazon.com/cdk/api/v2/docs/aws-cdk-lib.aws_apigateway.UsagePlanPerApiStage.html

      const usagePlan = new apigateway.UsagePlan(context, `UsagePlan`, {
        name: `UsagePlan`,
        description: `Usage Plan for API`,
        throttle: {
          rateLimit: 10000,
          burstLimit: 10000
        },
        apiStages: [
          {
            api: gateway,
            stage: gateway.deploymentStage,
            throttle: [
              {
                method: postMethod,
                throttle: {
                  rateLimit: 20,
                  burstLimit: 100
                }
              }
            ]
          }
        ]
      })