Bring a large pot of salted water to a boil. Cook pasta until just al dente. Drain and set aside.
In a large saucepan, melt butter over medium heat. Whisk in flour until smooth and bubbling, about 1–2 minutes.
Slowly whisk in warm milk. Stir constantly until sauce thickens, about 5 minutes.
Remove from heat. Stir in cheddar, mozzarella, and Parmesan until melted and smooth. Season with salt, pepper, and paprika.
Toss cooked pasta with cheese sauce. Serve immediately, or transfer to a baking dish, top with breadcrumbs, and bake at 375°F for 20 minutes until golden.
