Add an API Gateway REST API
We will add an API Gateway REST API with a one endpoint:
POST /dear-santa { gift: "lego" | "surprise", legoSKU?: "40499", from: "emmet" }

Update CDK stack

Edit the lib/eda-workshop-stack.ts file to look like this - adding your user name to the API name to identify it:
import { Construct, Stack, StackProps } from "aws-cdk-lib";
import { RestApi } from "aws-cdk-lib/aws-apigateway";
export class EDAWorkshopStack extends Stack {
constructor(scope: Construct, id: string, props?: StackProps) {
super(scope, id, props);
const api = new RestApi(this, "EDAWorkshopAPI-YOUR_USER_NAME");
const dearSanta = api.root.addResource("dear-santa");

Run a build

Take a look at the JavaScript files that get created:
npm run build

Synthesise the CloudFormation template

Take a look at the cdk.out/EDAWorkshopStack.template.json file that gets created, this is the CloudFormation template that will be deployed:
npm run cdk synth
Bonus: Add a simple test for your REST API to the eda-workshop.test.ts file and run npm test to execute it

Deploy CDK app

Now you can deploy your new CDK app (complete with an API!) to AWS - whenever you want to deploy your app just run this command and it will build and synthesise for you:
npm run cdk deploy

Test API endpoint

Once the CDK app has been deployed, you should see an API Gateway URL in the terminal. Use it to test out your API response:
curl -X POST https://{YOUR_API_URL}
You should get an "internal server error" - this is because we haven't got anything behind the endpoint yet.
So... let's put something behind the endpoint!
Bonus: Enable AWS X-Ray tracing for your REST API