Preheat oven to 450 degrees.
Place peppers, cut side up, on a rimmed baking sheet. Drizzle with olive oil.
Divide garlic among peppers. Sprinkle with oregano and season with salt and pepper.
Roast until flesh is tender and skin is blistered in spots, about 35 minutes.
Transfer peppers to a platter and top with a handful of torn basil leaves.