I have used three techniques to reduce facial fat:
1. Coolsculpting for double chin
2. Ultraformer/Ultherapy HIFU for face and neck areas
3. Threadlift for face and neck areas: PDO threads also cause a mild lipolysis and has the added advantage of lifting sagging tissues.
All three can be performed in that order for submental fat, with very good results.
If the big face is caused by bulky jaw muscles, botulinum toxins can also help with that.
Hope this helps!