Position a rack in the center of the oven and heat the oven to 425°F.
Put the oil and garlic in a small (8-inch) skillet and set over medium-low heat. Cook, stirring occasionally, until the garlic just begins to turn golden, 8 to 12 minutes. Strain the garlic and oil through a sieve set over a bowl; spread the garlic slices on a paper-towel-lined plate to drain.
Put the shrimp in a gratin or baking dish that is about 7×9 inches. Pour the garlic oil and wine over the shrimp and season with 1 tsp. salt and 1/4 tsp. pepper.
Roast, stirring once, until the shrimp are pink, opaque, and cooked through, 8 to 12 minutes. Sprinkle the garlic slices, basil, and lemon zest over the shrimp, stir to combine, and serve immediately.
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