4 Tbsp extra-virgin olive oil, divided
2 Tbsp balsamic or red-wine vinegar
1 Tbsp lime juice
⅛ tsp salt
freshly ground pepper to taste
1. Preheat oven to 400°F.
2. Rub off the excess papery skin from garlic without separating the cloves. Slice the tips off the head (or heads), exposing the ends of the cloves. Place the garlic on a piece of foil, drizzle with 1 tablespoon oil and wrap into a package. Put in a baking dish and bake until the garlic is very soft, 40 minutes to 1 hour. Unwrap and let cool slightly.
3. Squeeze the garlic pulp into a blender or food processor (discard the skins). Add the remaining 3 tablespoons oil, vinegar, lime juice, salt and pepper and blend or process until smooth.
To Make Ahead: Cover and refrigerate for up to 3 days.