Bring a large pot of water to a boil. Add 2 tablespoons salt and the pasta; cook 3 minutes less than package indicates. Drain.
Heat butter and oil in a large Dutch oven over medium heat about 1 minute. Add garlic and shallots; cook, stirring, until fragrant, about 2 minutes. Stir in chard, lemon zest, wine, 1 teaspoon salt, and the red pepper flakes; season with pepper. Cook, covered, stirring occasionally, until chard has just wilted, 2 to 3 minutes.
Stir in pasta, ricotta, and pine nuts. Cook, stirring occasionally, until pasta is al dente, 3 to 4 minutes. Divide among 4 serving dishes. Serve sprinkled with Parmesan.