https://twitter.com/brianleroux/status/1577979058700578816

Connect.yml

ConnectWSLambda:
  Type: AWS::Serverless::Function
  Properties:
    Handler: index.handler
    CodeUri: "/var/task/src/ws/connect"
ConnectWSRoute:
  Type: AWS::ApiGatewayV2::Route
  Properties:
    ApiId:
      Ref: WS
    RouteKey: "$connect"
    OperationName: ConnectWSRoute
    Target:
      Fn::Join:
      - "/"
      - - integrations
        - Ref: ConnectWSIntegration
ConnectWSIntegration:
  Type: AWS::ApiGatewayV2::Integration
  Properties:
    ApiId:
      Ref: WS
    IntegrationType: AWS_PROXY
    IntegrationUri:
      Fn::Sub:
      - arn:aws:apigateway:${AWS::Region}:lambda:path/2015-03-31/functions/${ConnectWSLambda.Arn}/invocations
      - {}
ConnectWSPermission:
  Type: AWS::Lambda::Permission
  DependsOn:
  - WS
  - ConnectWSLambda
  Properties:
    Action: lambda:InvokeFunction
    FunctionName:
      Ref: ConnectWSLambda
    Principal: apigateway.amazonaws.com