Heat the oil in a 10-inch cast iron skillet (or a similarly shaped ovenproof pan) over medium heat until the oil starts to shimmer, making sure to coat the sides and bottom.
Add the sausage and onions to the hot pan and sauté to a light brown, then set aside.
Combine the parsley, tomatoes, cheeses, salt and pepper, then blend with the eggs.
Pour the egg mixture into the hot skillet and incorporate the onions and sausage with a heat-resistant rubber spatula, lifting the egg mixture from the bottom of the pan 2 times to create layers.
Place the skillet into the oven and bake for 5–7 minutes or until the eggs are firm to touch and golden brown on top.
Remove from the oven and run a spatula around the skillet’s edge to loosen the frittata from the sides.
Invert the frittata onto a serving plate.
Cut it into quarters or sixths and garnish with a sprinkle of Parmesan cheese and basil sprig.