In a large shallow skillet, bring water to a boil and add a couple pinches of salt. Add spaghetti, making sure there’s just enough water to cover the pasta. While maintaining a low boil, cook until almost done, gently toss it around occasionally.
In another large skillet on low heat, add ground mixed peppercorns and cook for 2 minutes, shaking the pan often.
Stir in a couple ladles of pasta water to the peppercorns to prevent from burning and increase the heat to medium-low.
In a small bowl, combine Grana Padano and Pecorino cheese. Stir to blend and set aside.
When the pasta is almost cooked, transfer to the peppercorn mixture and stir to coat; reserve a ¼ cup pasta water for the cheese later.
To finish the spaghetti, add a couple ladles of pasta water from the skillet where the noodles were initially cooked and toss. When the liquid is all absorbed, add more (it’s the same technique as cooking risotto). Repeat until pasta is done.
Turn off the heat and let the noodles sit for a few minutes to cool off.
Meanwhile, add the reserved pasta water to the cheeses, a little at a time, and stir until the mixture resembles a paste. Another way of doing it is to add the cheeses to the jar of a blender and keep adding cooled pasta water until the mixture turns into a creamy mixture.
Add cheese paste to the spaghetti and stir until it gets creamy – add a touch more water if needed. If using the blender method, simply pour, stir and serve.
Serve immediately, add extra grated cheese and season with more black pepper.