Position a rack in the center of the oven and heat the oven to 400°F.
In a food processor, combine the garlic, shallots, 3 Tbs. of the oil, the vinegar, chili powder, cumin, oregano, sugar, 3/4 tsp. salt, and 1/4 tsp. pepper. Pulse for several seconds to make a paste.
Cut the tenderloin in half crosswise and then butterfly both halves by holding a knife parallel to the cutting board and cutting a lengthwise slit to within 1/2 inch of the other side of the tenderloin. Spread 1 Tbs. of the paste inside each slit. Tie with kitchen string or secure with toothpicks and season with salt and pepper.
Heat a heavy-duty, ovenproof, 10-inch skillet over high heat until hot and add the remaining 1 Tbs. oil, swirling the pan to coat the bottom. Add the tenderloins and sear on all sides until golden-brown, 3 to 4 minutes total. Transfer the skillet to the oven and roast for 8 minutes. Turn the tenderloins over and spread the remaining paste on top. Roast until an instant-read thermometer inserted in the thickest part of each registers 145°F, about 6 minutes more. Transfer to a cutting board, remove the string or toothpicks, and let rest for 5 minutes. Slice 1/2 inch thick and serve with the lime wedges.