Heat 1 tablespoon oil in a high-sided skillet over medium heat. Cook garlic until pale golden, about 3 minutes. Add 2 cups tomatoes and 1/2 teaspoon salt. Cook until soft, about 7 minutes. Add stock. Simmer until saucelike, about 1 minute. Add remaining cup tomatoes. Cook until warm, 1 to 2 minutes.
Meanwhile, bring a large pot of water to a boil. Cook pasta according to package instructions until al dente. Drain.
Toss pasta in skillet to coat. Stir in basil, reserving some for garnish.
Divide pasta among 4 plates. Top with any remaining sauce. Dot with ricotta, and drizzle with remaining teaspoon oil. Top with shaved cheese and remaining basil. Sprinkle with pepper.