Bring 4 quarts water to a boil in large Dutch oven or stockpot.
While water is heating, heat 12-inch heavy-bottomed skillet over high heat for 4 minutes.
Meanwhile, toss shrimp with half of red pepper flakes, 2 tablespoons olive oil, and ¾ teaspoon salt.
Add shrimp to hot skillet and quickly arrange in single layer; sear until bottom of shrimp forms small spot of crust, about 30 seconds.
Remove skillet from heat, turn shrimp over, and add cognac; pause until cognac has warmed slightly, about 5 seconds, and return to high heat.
Wave lit match over pan until cognac ignites, shaking pan.
When flames subside, 15 to 30 seconds later, remove shrimp to medium bowl and set aside.
Allow empty skillet to cool, off heat, for 2 minutes; return to burner over low heat; add 3 tablespoons olive oil and 3 tablespoons garlic and cook, stirring constantly, until garlic foams and becomes sticky and straw colored, 7 to 10 minutes.
Add remaining red pepper flakes and 3/4 teaspoon salt, sugar, tomatoes, and wine, increase heat to medium-high, and simmer until thickened and fragrant, about 8 minutes longer.
Stir in reserved shrimp (with 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.
Meanwhile, add pasta and 1 tablespoon salt to boiling water, stir to separate pasta, 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 (sauce only, no shrimp) and 2 to 3 tablespoons reserved pasta cooking water; toss to coat.
Divide pasta among warm serving plates, top with a portion of sauce and shrimp, and serve immediately.