Bring 2 quarts of water to boil in a large pot. Add fregola and cook over medium heat until al dente. Drain, reserve one cup of cooking liquid, and spread pasta on a sheet pan. Mix with half the olive oil and stir until cooled to room temperature. Hold. Heat rest of olive oil in a sauté pan until it shimmers. Add carrots, celery, shallots and garlic. Cook on medium heat until vegetables are tender and fragrant. Drop heat to a low simmer and hold. Season with salt and pepper to taste. Keep warm until serving.