Vercel supports rewrites which we can use as a reverse proxy. Create a vercel.json file and add a rewrites object from the /ingest route to https://app.posthog.com or https://eu.posthog.com.
Once done, set the /ingest route of your domain as the API host in your PostHog initialization like this:
Once updated, deploy your changes on Vercel and check that PostHog requests are going to https://www.your-domain.com/ingest by checking the network tab on your domain.