Heat the oil and butter in a 12-inch nonstick ovenproof skillet over medium heat.
Add in asparagus and sauté until tender, about 3-4 minutes.
Add the bruschetta and continue sautéing another 2-3 minutes, until warmed through.
Whisk together eggs, cream, salt, and pepper. Pour the egg mixture over the asparagus and bruschetta mixture. Sprinkle with cheese and cook until the frittata starts to set at the edges, about 3 minutes. Run a rubber spatula around the edge of the skillet to pull frittata away from the sides. This is going to help release it after we put it in the oven.
Place the skillet under the broiler until the top is set and golden brown, about 5 minutes. Let the frittata stand 2 minutes. Using a rubber spatula, loosen the frittata from skillet and slide the frittata onto a cutting board or plate.