Preheat oven to 425 degrees. Place peppers on a rimmed baking sheet; rub with 1 tablespoon oil. Roast until peppers are soft and skins have split, 30 to 35 minutes. Transfer peppers to a medium bowl. Cover bowl tightly with plastic wrap and let peppers steam 20 minutes.
Peel peppers, slice in half lengthwise, and remove ribs and seeds. Cut into 1-inch-wide strips and return to bowl. Add lemon zest and juice, garlic, oregano, salt, pepper, and 3 tablespoons oil and toss.
To store, refrigerate, up to 2 days.