Turn a stove burner on high heat. Place peppers on burner and roast 12 to 15 minutes, turning regularly with tongs so peppers char evenly. Place in a paper bag; seal and let stand (and steam) 5 minutes. Peel off blackened skin and discard. Cut peppers into quarters; remove and discard seeds and core.
Squeeze 4 cloves roasted garlic from their skins into a mortar. Add salt and 1/2 of the almonds, peppers, mint, and 1/2 of remaining olive oil. Using a pestle, crush against bottom and sides of mortar until a coarse paste forms.
Add remaining almonds, peppers, mint, and olive oil, crushing as directed. Stir in vinegar and ground pepper. Transfer to an airtight container, cover with a layer of extra-virgin olive oil, and refrigerate up to 5 days.
Note: This pesto can be made in a food processor: Simply combine the ingredients and blend 20 to 30 seconds, to a coarse paste. Chef Michela Larson prefers crushing them in a mortar with a pestle—a slower process, which she finds results in a more aromatic, flavorful pesto.