1. In a medium saucepan over medium heat, melt the butter. Add the shallot and cook, stirring often, until it begins to brown, about 3 minutes. Add the garlic and cook until fragrant, about 1 minute. Stir in the rest of the sauce ingredients, bring to a simmer, and reduce the heat to low. Simmer, stirring often, until slightly reduced, about 10 minutes. Transfer to a bowl to cool.
2. Lightly brush the steaks on both sides with the oil. Season evenly with the salt and pepper. Let the steaks stand at room temperature for 20 to 30 minutes before grilling. Prepare the grill for direct cooking over high heat.
3. Brush the cooking grates clean. Grill the steaks over direct high heat, with the lid closed as much as possible, until cooked to your desired doneness, 6 to 8 minutes for medium rare, turning once. Remove from the grill and let the steaks rest for 3 to 5 minutes. Serve the steaks warm with the sauce on the side.