Preheat grill to high heat. Lightly coat peppers with olive oil. Grill about 20 minutes, turning occasionally until evenly charred. Transfer to a bowl and cover with plastic wrap. Set aside about 10 minutes. Carefully remove plastic; let peppers cool slightly. Working quickly, gently scrape off skin. Core and seed peppers, reserving juices. Slice into 1-inch-wide strips. In a bowl, combine peppers, their juices, vinegar, 1 Tbsp. olive oil, and 1/4 tsp. salt. Set aside in a warm place.
Grill calamari over high heat about 1 minute per side, until lightly charred (the tentacles will char faster than the rest—that's okay). Shake cooking juices out. Toss mint into pepper mixture, and place on serving dish. Top with calamari, season to taste, drizzle with 1/2 Tbsp. olive oil, and serve.