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1
Heat 1 tablespoon oil in a large heavy pot over medium-high heat. Season oxtails with salt and pepper. Working in 2 batches, cook until browned on all sides, adding 1 tablespoon oil between batches, 10-15 minutes per batch; transfer to a plate.
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2
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.
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3
Using a slotted spoon, transfer oxtails to a plate. Let cool slightly; shred meat, discarding bones. Strain stock through a fine-mesh sieve into a large bowl or measuring cup (discard solids). Skim fat from stock; add water if needed to measure 4 cups. DO AHEAD:
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4
Cook cipolline onions in a large saucepan of boiling salted water until tender, 5-8 minutes. Drain and let cool. Trim root ends; peel and set aside.
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5
Heat butter in a large heavy pot over medium heat. Add red onions and cook, stirring occasionally, adding water by tablespoonfuls if pot becomes dry, until soft and deep brown, 45-60 minutes.
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6
Remove from heat; add bourbon and reserved cipolline onions. Return to heat and cook, scraping up browned bits, until bourbon is evaporated, about 4 minutes. Add chicken broth, barley, and reserved oxtail stock. Bring to a boil, reduce heat, and simmer, stirring occasionally, until barley is tender, 45-60 minutes. Season with salt and pepper. DO AHEAD:
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7
Add reserved oxtail meat to soup. Thin soup with water, if needed. Divide soup among bowls and serve with cornbread alongside.
