Meanwhile, toast bulgur in a large saucepan over medium heat, shaking the pan occasionally, until fragrant, about 5 minutes. Transfer to a bowl. Add the remaining 1/2 cup oil and onion to the pan. Cook, stirring occasionally, until the onion is softened, about 2 minutes. Reduce heat to medium-low, cover and cook, stirring occasionally, until the onion is very soft, 6 to 8 minutes.