Preheat oven to 350°F. Lay prosciutto slices on a parchment-lined baking sheet without overlapping or touching. Bake for 15-20 minutes or until crispy. Keep an eye on them to make sure they don’t burn or get too brown. Remove from oven and let cool completely. They will crisp more as they cool. Keep the oven on for the brussels sprouts.
Meanwhile, melt butter in a 12 inch ovenproof skillet, over medium-high heat. Add garlic and cook, stirring for 2 minutes or until just starting to brown. Remove garlic and discard.
Add shallots and cook, stirring for 1 1minute. Add brussels sprouts and season with salt and pepper. Cook for 5 minutes or until starting to brown. Keep stirring to a minimum to encourage browning.
Sprinkle flour over sprouts and stir for one minute. Slowly stir in chicken stock and then cream and dijon mustard. Bring to a boil and let simmer for one minute. Remove from heat and stir in Parmesan cheese.
Top with mozzarella and bake for 15 minutes or until brussels sprouts are tender when pierced with a paring knife.
Crumble proscuitto on top and serve.