Bring a big pot of water to a boil and add the pasta; cook until al dente, adding the peas for the last 3 minutes of cooking time. Before you drain it, scoop out some of the starchy cooking water with a measuring cup. Slice half a head of lettuce into about 1/2-inch wide ribbons.
Drain the pasta and peas and put it back in the pan. Add a knob of butter, a squeeze of lemon, the sliced lettuce and lots of freshly grated Parmesan cheese. Toss with tongs until the lettuce wilts, adding enough of the pasta water to make a saucy consistency. Serve with extra Parmesan at the table. Serves 2-4.