Preheat the oven to 300°F
Place an oven safe baking dish on the lower rack and fill it halfway with the boiling water from the kettle. This will create steam in the oven, which will help the egg bites to cook gently and attain a custardy texture
In a blender, combine the eggs, cottage cheese, Gruyère, cornstarch, salt, pepper, and hot sauce. Blend until completely smooth, about 30 seconds
Pour the egg mixture evenly into the prepared silicone muffin pan, filling each well about three-quarters full
Slice 6 pieces of prosciutto into tiny pieces. Divide the prosciutto pieces evenly over the egg bites. Using the sharp edge of a knife, press some of the prosciutto into the batter so it is not all floating on top
Bake for 20 minutes on the middle rack, until the eggs are set. You'll know they are done when the egg bites start pulling slightly away from the edges. Some of the egg bites may puff up and look a bit lopsided, but they will settle and deflate as they cool
Remove the egg bites from the oven and let rest in the pan for about 5 minutes. Use a small spoon to loosen the egg bites from the edges of the pan and carefully lift them out onto a plate. Serve warm
