Position a rack in the middle of the oven and preheat to 350 degrees F.
Toss the tomatoes with 1 tablespoon of the olive oil, garlic, vinegar, pepper flakes, and salt, to taste. Spread out on a baking sheet and roast until the tomatoes get juicy, about 15 minutes. Transfer tomatoes to a bowl and toss with the basil.
Dry the fish very well all over. To keep the fish from curling in the pan, lightly slash a cross-hatch pattern into the skin of the fish with a sharp knife. Brush the rounded flesh side of the fish with the remaining olive oil. Season with salt and pepper, to taste. Heat a large non-stick skillet over medium-high heat. Place the fish, seasoned side down, in the oil, and cook undisturbed over high heat, until the fish turns both opaque along the edges and golden on the bottom, about 3 minutes. Lightly salt the skin side of the fish. Flip the snapper and turn off the heat and let the fish cook in the residual heat of the pan until the fillets are firm but still juicy, about 1 minute more.
Divide the fish among 4 plates. Top with the tomatoes and serve.
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