Add remaining 1 tablespoon oil to same pot. Add shallots, carrots, and celery. Cook, stirring occasionally, until golden brown, 8-10 minutes. Add garlic; cook, stirring, just until fragrant, about 1 minute. Add wine; cook, scraping up browned bits, until reduced by half, 5-8 minutes. Add parsley, thyme, and 4 cups water; return oxtails to pot. Bring to a boil, reduce heat, cover, and simmer, stirring occasionally, until meat is fork-tender, 3-3 1/2 hours.