1. Bring 4 quarts water to rolling boil, covered, in large Dutch oven or stockpot.

2. While water is heating, heat 12-inch heavy-bottomed skillet over high heat for 4 minutes. Meanwhile, toss shrimp, half of red pepper flakes, 2 tablespoons olive oil, and 3/4 teaspoon salt in medium bowl. Add shrimp to skillet and quickly spread in single layer; cook, without stirring, until bottoms of shrimp turn spotty brown, about 30 seconds. Off heat, stir to turn shrimp, and add cognac; let stand off heat until cognac warms slightly, about 5 seconds, and return pan to high heat. Wave lit match over skillet until cognac ignites; shake skillet until flames subside, transfer shrimp to medium bowl, and set aside.

3. Off heat, cool now-empty skillet 2 minutes; return to burner and reduce heat to low. Add 3 tablespoons olive oil and 3 tablespoons garlic; cook, stirring constantly, until garlic foams and is sticky and straw-colored, 7 to 10 minutes. Add remaining red pepper flakes, 3/4 teaspoon salt, sugar, tomatoes, and wine; increase heat to medium-high, and simmer until thickened and fragrant, about 8 minutes. Stir in reserved shrimp and accumulated juices, remaining 1 tablespoon garlic, and parsley and simmer until shrimp have heated through, about 1 minute longer. Off heat, stir in remaining 1 tablespoon olive oil.

4. While sauce simmers, add linguine or spaghetti and remaining 1 tablespoon salt to boiling water, stir to separate pasta, cover, and cook until al dente; reserve 1/3 cup pasta cooking water and drain pasta. Transfer drained pasta back to now-empty Dutch oven or stockpot; add about 1/2 cup sauce (without shrimp) and 2 to 3 tablespoons reserved pasta cooking water; toss to coat. Divide pasta among warm serving bowls, top with a portion of sauce and shrimp, and serve immediately.