Preheat the oven to 400˚F.
In a large ovenproof skillet, heat the olive oil over medium-high heat.
Sauté the onion until soft and translucent, about 3-4 minutes.
Add the bruschetta to the skillet and allow it to cook with the onions for about 2 minutes to marry the flavors.
In a mixing bowl, whisk together the eggs, milk and parsley.
Pour the egg mixture into the skillet.
Stir to distribute the bruschetta and onions.
Stir in the shredded cheese.
Continue to stir the eggs, lifting the edges to allow uncooked egg underneath.
Once the bottom and edges are firm and the top is loose, about 5-7 minutes, bake the frittata.
Bake for 8-10 minutes, or until cooked through.
If desired, broil the frittata for 2-4 minutes to brown or melt extra cheese on top.
Remove from thge heat.
Using a rubber spatula, loosen the frittata from the skillet and slide the frittata onto a cutting board.
Cut the frittata into wedges.
Serve sprinkled with fresh parsley.