Bring 4 quarts water to rolling boil, covered, in stockpot. Stir in pasta and 1 tablespoon salt; cook until al dente, adding peas in last 15 seconds of cooking. Drain, reserving 3/4 cup cooking water, and return pasta and peas to stockpot.
Meanwhile, heat garlic, oil, and red pepper flakes in small skillet over medium heat; cook until sizzling but not browned, about 1 minute. Set skillet aside to cool slightly. Stir together ricotta, sun-dried tomatoes, Parmesan, mint, 1/2 teaspoon salt, 1/4 teaspoon pepper, and garlic/oil mixture in bowl. Stir pasta cooking water into ricotta mixture; add ricotta mixture to pasta in pot and stir well to combine. Serve immediately, passing additional Parmesan separately.