Now, let's create the API using a CloudFormation template. We will not discuss the components that were already discussed in previous recipes, nor will we discuss the theory for commands that were already discussed within the CLI commands section. The complete code is available in the code files:

1. Start to create the template with the version, description, and RestApi resource.

2. Add the proxy resource, '{proxy+}', as follows:

MyProxyResource:
  Type: AWS::ApiGateway::Resource
  Properties:
    RestApiId: !Ref MyRestAPI
    ParentId: !GetAtt MyRestAPI.RootResourceId
    PathPart: '{proxy+}'

3. Add the Method definition, with the AWS_PROXY integration type and ANY HTTP method, as follows:

MyMethod :
 Type : AWS::ApiGateway::Method
  Properties:
    AuthorizationType: NONE
    HttpMethod: ANY
    Integration:
      Type: AWS_PROXY
      IntegrationHttpMethod: POST
      IntegrationResponses:
      - StatusCode: 200
      Uri:
        !Sub
          - 'arn:aws:apigateway:${AWS::Region}:lambda:path/2015-03-31/functions/arn:aws:lambda:us-east-1:${AWS::AccountId}:function:${LAMBDA_NAME}/invocations'
          - LAMBDA_NAME: !ImportValue LambdaForProxyIntegration

    ResourceId: !Ref MyProxyResource
    RestApiId: !Ref MyRestAPI
    MethodResponses:
    - StatusCode: 200

4. Add the deployment resource in a stage: dev.
5. Provide permission to the API to invoke the Lambda, as follows:

LambdaInvokePermission:
  Type: AWS::Lambda::Permission
  Properties:
    FunctionName: !ImportValue LambdaForProxyIntegration
    Action: 'lambda:InvokeFunction'
    Principal: apigateway.amazonaws.com
    SourceArn: !Sub
       - arn:aws:execute-api:${AWS::Region}:${AWS::AccountId}:${API_ID}/*/*/{proxy+}
       - API_ID: !Ref MyRestAPI

6. Provide an Outputs section with a sample endpoint, as follows:

Outputs:
  SampleEndpoint:
    Description: 'Sample Endpoint'
    Value: !Sub
        - https://${API_ID}.execute-api.${AWS::Region}.amazonaws.com/dev/MyApp
        - API_ID: !Ref MyRestAPI

7. Execute the create-stack command to deploy the API.

Since we are importing the Lambda LambdaForProxyIntegration, the Lambda's CloudFormation template has to be executed first. 

8. Finally, test the API from a REST client, such as Postman (similar to what we did for the API that we created using the CLI commands). You can also use a browser for testing, which uses the GET method, as the API can accept any HTTP method.