Preheat oven to 375°F/190°C.
Heat oil in a sauté pan over medium heat until rim is hot to the touch. Add prosciutto and fry until golden brown. Remove from pan and set aside.
Add shallot and sauté until slightly caramelized.
Add red pepper and continue to sauté for another minute. Add garlic and sauté for about half a minute. Turn off heat and set pan aside.
In a medium-size bowl, whisk eggs, milk, thyme, salt and pepper. Fold in cubed bread and let stand 10 minutes.
Add shallot mixture and half the cheese to the egg mixture, stir well to combine.
Pour into a buttered casserole pan. Top with prosciutto pieces and bake for 30 minutes.
After 30 minutes, sprinkle with remaining Asiago cheese and bake until cheese on top has turned golden brown, about 10 minutes.
Remove from oven and allow to cool for 10 minutes.
Cut into wedges, garnish with chopped parsley and serve.