Cook the pasta as directed on the box in the salted water. Add the butter, salt, and pepper to a heavy bottomed, medium-sized pot or skillet. Heat over a medium heat.
Once the butter has melted add the flour and whisk until smooth, removing all lumps from the flour. Slowly pour the milk in and whisk until smooth again. Turn the heat up a bit to about medium-high.
Add ½ cup of grated Parmesan cheese, whisk until combined. Continue whisking until the sauce has thickened, 5 to 8 minutes. The sauce will thicken even further as it cools.
Pour the Alfredo sauce over the pasta and mix until the pasta is evenly coated. If you have cooked it in a skillet you can add the pasta to the skillet and toss to cover the pasta with the sauce.