Crack the eggs in a large bowl and stir in the pesto. Whisk until well combined. Add ghee (or preferred fat) to a large skillet and turn the heat to medium. Pour in the egg mixture and cook until done, stirring regularly, about 5 minutes. Take off heat.
Line a sheet tray with parchment paper. Lay 3 pieces of prosciutto together, slightly overlapping to form a tortilla-like base. You should get 8 total. Divide egg mixture evenly between all the prqoscuitti wraps. Fold the meat around the eggs and lay seam side down.
Cook in an air fryer for 8 minutes, flipping half way through. (For this I lined a 8x8 pan with parchment paper and placed them on that.) OR Preheat the oven to 375° and bake 16-18 minutes, flip over and bake 5 more minutes.
These can be prepared and baked the morning of serving.