Preheat oven to 350 degrees. Spread almonds in a single layer on a rimmed baking sheet; toast in oven until lightly golden and fragrant, 7 to 8 minutes. Remove from oven, and let cool 15 minutes.
Meanwhile, roast red peppers over a gas burner until blistered and charred, turning as each section blackens. (Alternatively, roast peppers on a baking sheet under the broiler.) Transfer to a large bowl, and cover tightly with plastic wrap; let steam about 15 minutes. Using paper towels, peel off blackened skins; remove and discard stems and seeds.
Raise oven to 375 degrees. In a food processor, combine almonds, garlic, roasted red peppers, 3/4 teaspoon salt, paprika, mint, and vinegar. Process to a coarse paste, about 1 minute. With machine running, add 1 tablespoon oil in a slow, steady stream until sauce is smooth. Transfer sauce to a small bowl, and set aside.
Place potatoes on a rimmed baking sheet, and toss with remaining 1/2 tablespoon oil and 1/4 teaspoon salt. Roast in oven until skins are slightly crisp and potatoes are tender, shaking pan once to turn potatoes, 20 to 30 minutes. Serve hot with sauce on the side.