Go ahead and tell me, I’m interested

Indulge me also refers to sarcasm. "humour me"

If they say it, just that, "Indulge me," it's in answer to an objection. "But it will take too much time!" "But you already know this!" "But we did it ten times already!" It acknowledges that the request might be going overboard but please do it anyway.

You could also say "gratify/humor me"