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1
Bring 4 quarts water to a boil in large Dutch oven or stockpot.
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2
While water is heating, heat 12-inch heavy-bottomed skillet over high heat for 4 minutes.
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3
Meanwhile, toss shrimp with half of red pepper flakes, 2 tablespoons olive oil, and 3/4 teaspoon salt.
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4
Add shrimp to hot skillet and quickly arrange in single layer; sear until bottom of shrimp forms small spot of crust, about 30 seconds.
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5
Remove skillet from heat, turn shrimp over, and add cognac; pause until cognac has warmed slightly, about 5 seconds, and return to high heat.
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6
Wave lit match over pan until cognac ignites, shaking pan.
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7
When flames subside, 15 to 30 seconds later, remove shrimp to medium bowl and set aside.
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8
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.
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9
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.
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10
Stir in reserved shrimp (with accumulated juices), remaining 1 tablespoon garlic, and parsley and simmer until shrimp have heated through, about 1 minute longer.
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11
Off heat, stir in remaining 1 tablespoon olive oil.
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12
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.
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13
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.
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14
Divide pasta among warm serving plates, top with a portion of sauce and shrimp, and serve immediately.
