For the aioli, chop the garlic and chipotle pepper together on a cutting board to make a coarse paste. Place the paste in a food processor, add the lime juice and roasted red peppers, and purée. Add the mayonnaise, 1/4 teaspoon salt, and 1/4 teaspoon black pepper and process until smooth. Set aside.
For the salmon, place a large (12-inch), dry cast-iron skillet over high heat for 5 minutes. Place the salmon fillets on a board, pat dry with paper towels, and rub all over with olive oil. With the fillets rounded side up, sprinkle them with 1 1/2 teaspoons salt and 3/4 teaspoon black pepper.
Place the salmon in the skillet rounded side down and cook over medium-high heat for exactly 2 minutes without moving! Using a large metal spatula, turn the fillets rounded side up and place the skillet in the oven. Roast for 3 to 4 minutes, until the centers are rare. Cover the pan loosely with aluminum foil and allow the salmon to rest for 3 to 4 minutes for medium-rare or 5 minutes for medium. Serve the salmon hot with the aioli and a wedge of lime for squeezing.
The aioli will keep in the refrigerator for at least 5 days.