Bring a large pot of salted water to a boil. Add the spaghetti and cook until al dente, 8 to 10 minutes.
While the pasta cooks, mash the soft butter with the olive oil and pecorino cheese in a large bowl to form a paste.
When the pasta is tender, drain it, reserving ½ cup of the pasta cooking water. Add the spaghetti directly to the bowl with the butter mixture. Toss well to coat, adding the pasta water as needed to make a thick, creamy sauce that coats the pasta strands. Season with salt and lots of freshly ground black pepper.
Divide the pasta among four plates; serve immediately.