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Cook 1 lb. medium tube-shaped pasta (such as rigatoni or penne) in a large pot of boiling salted water, stirring occasionally, until al dente. Drain, reserving 2 cups pasta cooking liquid.
Meanwhile, pat 1 lb. large shrimp, peeled, deveined, dry with paper towels; season lightly with kosher salt. Heat ¼ cup extra-virgin olive oil in a large Dutch oven or other heavy pot over medium. Add 6 garlic cloves, finely chopped, ¼ cup finely chopped preserved lemon, and ½ tsp. crushed red pepper flakes and cook, stirring often, until preserved lemon is softened, about 2 minutes. Add shrimp and cook, stirring often, until just opaque, about 2 minutes.
Add pasta, 2 Tbsp. unsalted butter, cut into 2 pieces, and 1 cup pasta cooking liquid and cook, tossing vigorously, until butter is melted and sauce is thickened slightly, about 2 minutes. Add ½ cup finely grated Parmesan; toss until melted. Add ½ cup pasta cooking liquid, 2 Tbsp. unsalted butter, cut into 2 pieces, and ½ cup finely grated Parmesan and cook, stirring vigorously and adding more pasta cooking liquid if needed, until sauce is thickened and coats pasta, about 1 minute. Mix in 1 Tbsp. fresh lemon juice and ⅓ cup finely chopped parsley.
Divide pasta among shallow bowls. Top with more finely grated Parmesan and finely chopped parsley.