In a medium pan over medium heat, add olive oil, chopped garlic, rosemary sprig, and salt. Sauté gently until garlic has softened and rosemary has released its fragrance, about 5–6 minutes. Do not let it get to a boil! Add vinegar and bring to a simmer. Reduce the heat to medium-low and let the sauce reduce to ⅓ of the original volume. Stir occasionally.
Remove the olive oil mixture from the heat and discard the rosemary sprig. Season with salt and pepper, to taste. Finish with extra virgin olive oil, stirring in to form a loose paste. Keep warm until ready to use.
