Preheat oven to 375F and place rack in the middle of the oven. Bring a large pot of water to a boil for pasta, salt water and cook pasta to al dente.
While the pasta water comes to a boil, place a medium pot over medium-low heat with 2 turns of the pan of EVOO, about 2 tablespoons, and the butter. Add the onion and garlic to the pan and cook the veggies until very soft, about 10 minutes.
Turn the heat up to medium-high and sprinkle the flour into the pan. Cook for about 1 minute then whisk the wine into the pan, cooking for another minute to burn off the alcohol. Whisk the milk into the pan and bring up to a bubble. Add the nutmeg, spinach, artichokes, salt and pepper to the sauce and simmer until thickened and vegetables are warmed through, 2-3 minutes more. Add 1 cup of each of the cheeses to the sauce and stir until melted.
Toss the prepared sauce with the cooked pasta and transfer to a casserole dish. Sprinkle some more Fontina and Parmigiano over the top and bake until the cheese has melted and the top is golden brown, about 30 minutes.