Begin by preheating an outdoor grill to high heat and lightly oiling the grate. Subsequently, reduce the grill heat to medium.
Grill the whole red, yellow, and orange bell peppers on the preheated grill, turning them approximately every five minutes until they are charred on all sides. After grilling, transfer the charred peppers into a resealable plastic bag and seal it tightly. Allow the peppers to cool in the bag.
In a 1-pint glass jar (or a larger one if necessary), combine the olive oil, minced garlic, sliced basil, dried oregano, salt, and ground black pepper.
Once the peppers have cooled, remove them from the bag and carefully scrape off the charred skin. Cut the peppers in half, discarding the seeds and stems. Slice the peppers into long strips and place them into the jar with the oil mixture. Ensure the peppers are thoroughly coated in the oil.
Serve the roasted peppers as desired, storing any leftovers in the refrigerator for up to five days for optimal freshness.