- Bring 3 quarts of water to a boil in a 5-quart pot. Season with salt.
- Add pasta and cook, stirring occasionally, until about 2 minutes before tender. Drain, reserving 3/4 cup of the pasta cooking water.
- Heat the olive oil over medium heat in a Dutch oven (or another large pot or skillet). Add pepper and cook, swirling pan, until toasted, about 1 minute.
- Add 1/2 cup of the reserved pasta water to the pan and bring to a simmer. Add the pasta and the butter.
- Reduce the heat to low and add the Grana Padano or Parmesan, stirring and tossing with tongs until melted.
- Remove pan from heat. Add Pecorino, stirring and tossing until cheese melts, sauce coats the pasta and the noodles are al dente.
- Add more pasta water if the sauce seems dry. Transfer pasta to warm bowls and serve.