Place peppers, onion, dates, basil, parsley, tomato, bouillon powder, and garlic in the bowl of a food processor; pour in the oil. Pulse mixture until finely chopped, adding more oil if needed to thin; season with salt.

Pour pepper mixture into a small saucepan; bring to a boil. Squeeze lemon juice into pepper mixture, reduce heat to low, and simmer for 15 minutes.

Allow pepper mixture to cool; pour into a glass jar with a lid. Store pepper sauce in the refrigerator.