Bring a large pot of salted water to a rolling boil, then add the pasta and cook until just al dente, about 8 minutes. Drain quickly and set aside.
In your saucepan, melt the butter over medium heat until it smells nutty and turns a light golden brown, about 2-3 minutes.
Pour in the milk and whisk constantly as it warms, until it steams gently with small bubbles around the edges, about 10 minutes.
Add the grated cheddar cheese in small handfuls, stirring continuously until each addition melts into a smooth, creamy sauce. The cheese should be gooey and silky.
Season the sauce with salt, pepper, and paprika, tasting and adjusting as needed for flavor.
Fold the drained pasta into the cheese sauce, tossing gently to coat every noodle evenly and create a luscious, cheesy mixture.
If desired, transfer the mixture to a baking dish and broil at 200°C (392°F) for 3-5 minutes until the top is bubbly and golden brown.
Let the dish sit for 5 minutes to thicken slightly and allow flavors to meld. Serve hot, with extra cheese or herbs if you like.