Fill a large stockpot with water and bring to a boil. Add plenty of salt (I use 2 TB for a large potful) and the pasta, cooking until the pasta is almost, but not quite, al dente. Reserve 1/2 cup of pasta water.

When the pasta is almost done, heat a large skillet over medium flame. Melt 2 TB butter and add the freshly ground pepper, cooking until it is lightly toasted, about a minute. Splash in about 1/4 cup of the pasta water and the remaining 2 TB of butter and continue to cook the sauce until it begins to thicken slightly, another minute or so.

Drain the pasta and add it immediately to the sauce, along with the grated cheese. Working quickly, toss the pasta and sauce with tongs until the cheese is melted and the sauce coats the pasta uniformly (if it seems too dry, add a bit more pasta water). Remove pan from the burner and stir in the peas, which will cook quickly from the residual heat. Sprinkle the basil over the pasta and toss once more.

Serve immediately in warm bowls, topping with a little more cheese and chopped basil.