How to repair peeling on cabinets

Hi folks,

I want to refinish and paint my kitchen cabinets, but before touching the doors I want to ask opinions on how to repair this peeling on edges of 3 cabinets. Looks like steam from the range and kettle did this.

I was thinking to trim off the excess bit that has peeled and expanded, then sand down and fill with wood/general filler before painting with bullseye 123. Is there a better approach?