Place rack in upper third of oven and preheat to 350℉.
Line muffin pan with six cupcake liners.
Drape two slices of prosciutto into each cup liner, ensuring there are no holes for egg to sneak through. Note: The prosciutto will shrink a bit as it bakes so feel free to let the prosciutto drape over the cup liner a bit.
Place one tomato slice in each cup. Sprinkle 1 tablespoon of Parmesan on each tomato. Crack one egg into each cup.
Sprinkle each cup with fresh cracked black pepper to taste.
Bake 14 to 16 minutes, or until eggs are cooked as desired.
Top with chives. Cool 5 minutes before serving warm.