Heat the fat in the bottom of a large Dutch oven over medium-high heat. Add the onion, celery, carrots, and garlic. Season well with salt and pepper. Cook, stirring occasionally, until the vegetables have softened, about 10 minutes. Add the tomato paste and stir to coat the vegetables. Cook until the tomato paste darkens and sticks a bit to the bottom of the pot, about 2 minutes more.