Step 1Cook capellini in large pot of boiling salted water according to package directions until just barely tender, 2 to 3 minutes. Do not overcook, as it cooks further before serving. Reserve 1 1/2 cups cooking liquid, then drain capellini.
Step 2Heat oil in large skillet over medium heat. When hot, add garlic, lemon juice, 3/4 teaspoon salt and red pepper flakes. Cook until garlic is fragrant, about 20 seconds. Add hot pasta. Toss together, adding reserved cooking liquid as needed to moisten mixture. Cook until heated through, about 3 to 5 minutes. Toss with cheese. Taste and adjust seasoning and lemon juice. Serve immediately on hot plates, garnished with lemon wedges. Pass cheese separately.