Preheat oven to 400 degrees. In a large skillet, heat oil over medium. Add onion and carrots; season with salt and pepper. Cook, stirring occasionally, until tender, 6 to 8 minutes. Add beef, and cook, breaking up meat with a wooden spoon, until no longer pink, 3 to 5 minutes. Add tomato sauce; bring to a boil, reduce to a simmer, and cook, stirring occasionally, until meat mixture has thickened, 8 to 10 minutes; set aside.