Creating a cloudfront function in typescript using the CDK

I am trying to figure out how to write a cloudfront edge function in typescript using cdk 2.94.0. The way you specify these functions is weirder than a regular lambda you'd use with some other service like API Gateway. In this case, what i get is:

Error: Asset must be a .zip file or a directory (C:\work\i4academy\lib\redirect-handler.ts)

That's telling me that it won't really work with a higher level function wrapper like NodejsFunction. Unfortunately, that's what I need if I'm starting with typescript, as I need something to compile the typescript into javascript then build an appropriate distribution .zip.

I think I'm close to having this, just not quite figuring out the last piece, which is to make cloudfront use the lambda:

        const fnRole = new iam.Role(this, "redirect-function-role-id", {
            roleName: "redirect-function-role",
            assumedBy: new iam.ServicePrincipal('lambda.amazonaws.com')
        })
        fnRole.grantAssumeRole(new iam.ServicePrincipal('edgelambda.amazonaws.com'))

        const fnOpts: NodejsFunctionProps = {
            // ...props.baseLambdaConfig.baseLayers,
            functionName: "",
            runtime: lambda.Runtime.NODEJS_LATEST,
            bundling: {
                minify: true
            },
            entry: path.join(__dirname, "redirect-handler.ts"),
            handler: "handler",
            role: fnRole,
            architecture: lambda.Architecture.ARM_64,
            memorySize: 128,
            timeout: cdk.Duration.seconds(2),
            reservedConcurrentExecutions: undefined /* impacts cost */,
        }
        const redirectFunction = new nodejs.NodejsFunction(this, "redirect-function-id", fnOpts);


        const cfdist = new cloudfront.Distribution(this, 'cloudfront-dist', {
            defaultBehavior: {
                origin: new origins.HttpOrigin("www.something.com"),
                functionAssociations: [{
                    function: redirectFunction,
                    eventType: cloudfront.FunctionEventType.VIEWER_REQUEST,
                }]
            },
        });

I'm thinking maybe this is not possible if I want to use a cloud function. I think I could convert it to a lambda@edge but it would be six times the cost per request. That should not really be necessary, it's a really simple function - it looks at the incoming request then makes a decision about where to 301 redirect.

So is it even possible to write a cloudfront function (not lambda@edge) in typescript?