Combine salad oil, sugar, vinegar, tomato soup, Worcestershire sauce, and mustard in a saucepan.

Cook the sauce ingredients together over medium heat until well combined and slightly thickened.

Parboil the carrots until they are slightly tender but still firm.

Slice the parboiled carrots into thin rounds.

Spray a baking dish with cooking spray (Pam).

Layer the sliced carrots, onion, and peppers in the prepared baking dish.

Pour the cooked sauce over the layered vegetables, ensuring all are coated.

Cover the dish and refrigerate for 3 to 4 days to allow flavors to meld.