Place 4 quarts water in a stockpot; bring to a boil over high. Add 1⁄4 cup of the salt, and stir until dissolved. Add pasta, and cook until al dente, about 9 minutes. Drain. Reserve 1 cup cooking water; set aside with pasta.

Heat oil in a large skillet over medium-high. Add shrimp; sprinkle with pepper and 1⁄2 teaspoon of the salt. Cook, stirring occasionally, until shrimp are partially opaque, about 30 seconds. Add wine and garlic; continue cooking, stirring occasionally, until shrimp are mostly cooked through, about 1 1⁄2 minutes.

Add pasta and 1⁄4 cup of the cooking water; bring to a simmer. Add butter, lemon juice, and remaining 1 teaspoon salt. Cook, stirring constantly, until sauce thickens and coats pasta, about 1 minute, adding more cooking water, 1⁄4 cup at a time, if needed. Remove from heat. Stir in torn basil. Top with lemon peel strips, basil leaves, and black pepper.