Toast the peppercorns in a hot, dry frying pan until aromatic. Cool and then grind coarsely in a mortar and pestle or a spice grinder.
Bring a wide saucepan of water to a boil. Season it very well with salt. The water should taste as salty as the sea. To know how much water, the pasta should be covered but only just as we want maximum starchiness in that water at the end of the cooking time.
Once the water is rapidly boiling. Add the pasta, occasionally stirring to ensure it doesn't stick. Cook for a minute or two short of the suggested cooking times on your pasta packaging. The pasta should be a little less than al dente.
Strain the pasta (reserving 250ml of the hot starchy water).
Drain the pasta and leave it & the water to cool for a minute or two.
Melt approximately 2/3 of the butter with olive oil in a large frying pan over medium heat. While the butter is melting, add the freshly grounded pepper. Stir or swirl the pan for a minute or so. The butter should be fully melted.
Turn the heat to very low.
Carefully whisk in 200ml reserved pasta water.
Add the pasta into the pan with the melted butter & pepper. Toss briefly.
Scatter over the cheese, but don't stir. Wait for 30 seconds for the cheese to melt. Then toss well. This prevents the cheese from clumping. Loosen with the remaining pasta water, if required.
Serve in warm bowls.
Sprinkle a little additional freshly ground pepper or Aleppo pepper flakes, if you choose.
Cacio e Pepe must be served warm and enjoyed immediately.