Preheat oven to 375f and set a rack on the middle level and the other rack near the top.
Bring a large pot of salted water to boil and cook the spaghetti until 2 minutes less than al dente.
Meanwhile, in a large bowl, beat together the eggs, milk, 1 teaspoon kosher salt, and black pepper. Add 1 ½ cups Fontina, and a ½ cup of Pecorino Romano cheese and stir to combine.
Heat a 10-inch oven-proof or ideally a cast iron pan to medium heat.
Drain the spaghetti and add to the bowl. Mix well to combine.
Add the butter and oil to the hot pan and spread to coat the whole pan. Add the spaghetti mixture to the pan and cook for 1 minute without stirring then turn off the heat.
Top with the remaining Fontina and Pecorino and bake for 12-15 minutes in the center of the oven or until the spaghetti pie is set. For a browner top, move the pan to the upper rack and broil for 1-2 minutes but watch carefully.
Let the spaghetti pie sit for 5 minutes before cutting it into slices. Enjoy!