HTTP API doesn't forward Cookies to Lambdas

Cookie headers are not forwarded to Lambdas

$ curl -H "Cookie: test" https://redacted.execute-api.us-east-2.amazonaws.com

{"accept":"*/*","content-length":"0","host":"redacted.execute-api.us-east-2.amazonaws.com","user-agent":"curl/7.58.0","x-amzn-trace-id":"Root=1-5ed6b365-97645c08fe07add8b0a75568","x-forwarded-for":"redacted","x-forwarded-port":"443","x-forwarded-proto":"https"}

Lamda

exports.handler = async (event) => {
    const response = {
        statusCode: 200,
        body: JSON.stringify(event.headers) ,
    };
    return response;
};