When setting up CORS in API Gateway with CDK, the preflight request results in 500 InternalServerErrorException

We set up CORS according to https://docs.aws.amazon.com/cdk/api/v2/python/aws_cdk.aws_apigateway/Cors.html

apigateway.RestApi(self, "api",
    default_cors_preflight_options=apigateway.CorsOptions(
        allow_origins=apigateway.Cors.ALL_ORIGINS,
        allow_methods=apigateway.Cors.ALL_METHODS
    )
)

After deployment, CDK automatically creates OPTIONS method to all endpoints.

When making a preflight request with curl -X OPTIONS https://hostname/path/to/endpoint we receive following response

< HTTP/2 500 
< date: xxxxxxxxxxxxx
< content-type: application/json
< content-length: 36
< x-amzn-requestid: xxxxxxxxxxxxxx
< x-amzn-errortype: InternalServerErrorException
< x-amz-apigw-id: xxxxxxxxxxxxxxxxxxx
< x-amzn-trace-id: xxxxxxxxxxxxxxxxxxxxxxxx

In CloudWatch, we see following log:

HTTP Method: OPTIONS, Resource Path: /path/to/endpoint                                                                                 
Execution failed due to configuration error: Unable to transform request                                                                
Method completed with status: 500

What is the cause of the problem and how can we fix it?