In a large skillet, heat butter and olive oil over medium heat. Add onions and cook, stirring occasionally for 10 minutes until softened and lightly browned. Add salt, pepper and granulated sugar and continue to cook for another 10 minutes. If onions begin to burn, lower heat.
Preheat oven to 350 degrees.
In a large bowl, whisk together eggs, milk, mustard and cornstarch. Set aside.
Brush a 9-inch round cheesecake pan with a removable bottom with some of the melted butter. (You can also use a 9-inch round baking pan) Brush top of phyllo sheet lightly with some of the melted butter keeping the other sheets covered with a kitchen towel, so they don't dry out. Press phyllo sheet into pan, buttered-side down. Repeat with remaining phyllo sheets, overlapping to completely cover bottom and up sides of pan.
Add half of the Swiss and half of the Jarlsberg cheeses along with half of the onions to the pan. Gently pour the egg mixture over the cheeses. Add the remaining shredded cheeses, onions and prosciutto. Mix gently with a knife. Sprinkle top of quiche with 1-2 tablespoons Parmesan cheese.
Bake for 45-50 minutes or until the quiche is lightly browned on top and the center is set. Remove from oven and let cool just slightly before cutting in wedges. Serve with a side salad if desired.