Make aioli: Pulse garlic in the bowl of a food processor until it is finely chopped. Add egg yolks and mustard, and season with salt; process until mixture is blended. With machine running, add half the canola oil, a few drops at a time, until mixture is emulsified. Add 4 teaspoons lemon juice. With machine running, add remaining canola oil and the olive oil. Season with salt and lemon juice. Transfer to a bowl; refrigerate, covered, up to 2 days.
Season shrimp with pepper. Place a large cast-iron skillet over medium heat; lightly cover bottom with salt. Arrange half the shrimp in a single layer. Place a pan on top as a weight; cook 2 minutes. Remove top pan, and turn shrimp; cook until they are pink, about 1 1/2 minutes. Transfer to a plate; wipe pan with a dry paper towel. Repeat with remaining shrimp. Serve with aioli.
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