Fill a large pot with lightly salted water and bring to a rolling boil over high heat. Once the water is boiling, stir in the gemelli, and return to a boil. Cook uncovered, stirring occasionally, until the pasta has cooked through, but is still firm to the bite, about 8 minutes.
Drain well in a colander set in the sink.
Add olive oil, and toss pasta until coated; set aside.
Heat a large skillet over medium-high heat and stir in the ground beef. Season with salt and black pepper. Cook and stir until the beef is crumbly, evenly browned, and no longer pink, about 10 minutes.
Drain and discard any excess grease. Set aside.
Preheat an oven to 350 degrees F (175 degrees C).
Heat 3 tablespoons butter and the flour in a large skillet over low heat. Cook and stir until the butter is melted and the flour is incorporated, then slowly whisk in the milk. Stir in the fontina cheese, sharp Cheddar cheese, white Cheddar cheese, and 1/4 cup Parmesan cheese; cook, whisking constantly, until cheese is melted and sauce is thickened, about 5 minutes. Season with paprika, nutmeg, garlic powder, cinnamon, and chili powder. Season to taste with salt and black pepper. Stir in the pasta and beef, and transfer mixture to a large baking dish.
Combine 2 tablespoons butter, bread crumbs, and the remaining 2 tablespoons Parmesan cheese in a bowl.
Sprinkle mixture over the pasta in the baking dish.
Bake in the preheated oven until bubbly, about 12 minutes, then set the oven on broil. Broil until lightly browned, about 3 more minutes.
