Spray the bottom and sides of an 8x8-inch baking dish with cooking spray.

Place cubed bread into the prepared pan. Add 2 cups fontina cheese, prosciutto, tomatoes, and basil. Combine until ingredients are evenly distributed.

Whisk eggs in a bowl and add half-and-half, parsley, tarragon, salt, and pepper. Pour egg mixture over bread mixture. Cover the baking dish with plastic wrap and chill 8 hours to overnight.

Remove the baking dish from the refrigerator 20 minutes before baking.

Meanwhile, preheat the oven to 350 degrees F (175 degrees C).

Remove the plastic wrap from the baking dish and top with remaining 1 cup fontina cheese. Cover with aluminum foil.

Bake in the preheated oven until cheese has melted and beginning to brown, egg mixture is browned and bubbly, and a knife inserted into the center comes out clean, about 15 minutes. Let sit 5 minutes before serving.