Fill a large pot with water, add a couple of pinches of Kosher salt, and bring to a boil.
Cook the pasta according to the package instructions, reserving 1 cup of the pasta liquid before draining (important!)
In a large skillet, heat the butter and oil over medium-high heat until the butter has melted into the oil. Add the pepper; cook and stir about 1 minute, just until the pepper is a little bit toasted. Add the cooked pasta to the skillet and 3/4 of the reserved cooking liquid, tossing to coat. Sprinkle the Parmesan on top and continue to cook, tossing, until the cheese is melted and the pasta is well-coated (about 2 minutes). Add a little more of the cooking liquid, as needed, to bring moisture back into the pasta and loosen it up. Season with salt, and divide the pasta between 4 bowls. Sprinkle additional Parmesan cheese on top.