Preheat the oven to 375 F, and thoroughly grease a muffin pan with non-stick spray.
Arrange the prosciutto slices in the muffin pan, to form little cups.
Sprinkle half of the Parmesan cheese into the prosciutto cups.
Carefully crack the eggs into the prosciutto cups, taking care not to break the yolks.
Sprinkle the remainder of the Parmesan cheese over the eggs, and sprinkle with thyme.
Bake the egg cups for 10-15 minutes, depending on how runny or firm you like the egg yolks.10 min: Runny11-12 min: Soft/Runny12-15 min: Soft Set15-18 min: Firm
Cool in the pan for 1 minute, then use a spoon to scoop the egg cups out of the pan. Serve immediately with hot, buttered toast.
Since the prosciutto and Parmesan are already salty, these really don't need any added salt. Season to taste with salt and pepper, if desired.