Bring a medium pot of salted water to a boil. Add the pasta and cook just shy of al dente. (We're going to cook the pasta for 1-2 minutes later.) Reserving 1/4 cup pasta water, drain the pasta in a colander and set both aside.
To a medium skillet, toast the peppercorns until they become fragrant, about 2 to 3 minutes. Transfer them to a mortar and pestle and crush until coarse. Alternatively, you could transfer the peppercorns to a pepper grinder, OR you could wrap the peppercorns in plastic wrap and crush the heck out of them with the back of a skillet (that isn't hot!).
To the same medium skillet, melt the butter with the olive oil over medium heat. Add a few pinches of pepper, 2 tablespoons pasta water and cheese; stir continuously until the cheese is melted and the sauce starts to come together, about 2 minutes. Decrease the heat to medium-low, add the pasta to the skillet and toss gently in the sauce until evenly coated. The cheese will be slightly clumpy; using a fork, stir the pasta vigorously for an additional minute or so, until the clumsiness disappears. If the pasta is slightly dry, add a teaspoon or two of pasta water until it's the consistency of your liking. Serve immediately and top with a sprinkle more of pepper and a few small (or large!) pinches of cheese.