Cover 4 phyllo pastry sheets with a damp tea towel to prevent them from drying out and becoming difficult to work with. On clean surface area, place first sheet down and lightly brush with avocado oil; place second sheet on top and continue process with all 4. With sharp knife, press blade into the pastry to cut (as opposed to using a back-and-forth motion, which may tear the pastry) into 12 equal squares.
Lightly brush muffin tin with avocado oil, then place each phyllo square into muffin tin, carefully pushing the pastry down into the edges. Spoon approximately 1/4 cup turkey filling into each. Slice brie cheese into 12 equal pieces and place on top of turkey. Bake in preheated oven for 15 minutes, or until golden brown and cheese is melted.
Once baked, let cool for 5 minutes in muffin tins, then remove and serve warm topped with cranberry sauce.