Here's a screenshot showcasing my problem:
I found some resources on this issue, but for some reason, it's not working for me. I'm using the Inset tool, and setting the depth to a negative number.
Do I need edge loops first for that to work? There's no way for blender to create vertices at the right spot automatically?

@Leander cool, but it's only for 2.79, not 2.8, correct? Otherwise that'd be exactly what Im looking for indeed.
– Robin Jun 07 '20 at 12:28