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1
Season chicken all over with salt and pepper. Place in a large bowl and add yellow onion, carrot, thyme, bay leaves, and wine. Cover and chill, turning chicken once or twice, at least 1 day and up to 2 days.
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2
Remove chicken from marinade (do not discard) and pat dry with paper towels; pluck off any aromatics still stuck to chicken. Strain marinade through a fine-mesh sieve into a large bowl and set infused wine and aromatics aside separately.
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3
Heat 1 Tbsp. oil and 1 Tbsp. butter in a large Dutch oven or other heavy pot over medium. Add bacon and cook, stirring often, until brown and crisp, 5-8 minutes. Using a slotted spoon, transfer to a medium bowl.
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4
Arrange chicken, skin side down, in a single layer in same pot and cook until skin is browned, 8-10 minutes. Transfer to a plate and arrange skin side up.
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5
Pour off all but 3 Tbsp. fat from pot and increase heat to medium-high; reserve fat for another use. Add mushrooms and cook, tossing often and adding a splash of infused wine if bits stuck to bottom of pot are getting too dark, until browned and tender, about 5 minutes. Transfer mushrooms to bowl with bacon.
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6
If bottom of pot is dry, add a tablespoon or so reserved fat and cook reserved aromatics, stirring often, until vegetables are soft and browned around the edges, 8-10 minutes. Sprinkle flour over top and cook, stirring, until flour is no longer visible. Return chicken to pot, arranging skin side up in a single layer, and pour in reserved infused wine (it should come just to the top of the chicken pieces; add water to get it there if needed). Bring liquid to a gentle simmer, partially cover pot, and cook chicken until an instant-read thermometer inserted into the thickest part of breast registers 160u00b0F, 30-40 minutes.
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7
Meanwhile, heat remaining 2 Tbsp. oil and 1 Tbsp. butter in a medium skillet over medium. Add pearl onions, season with salt, and cook, shaking skillet often, until onions are browned all over, 8-10 minutes. Add water to barely cover onions and partially cover skillet. Bring to a boil, reduce heat, and simmer until onions are tender all the way through, 15-20 minutes; set aside.
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8
Transfer chicken to a platter and tent with foil. Strain braising liquid through a fine-mesh sieve into a large bowl; discard solids. Return liquid to pot and set over medium heat. Whisk vinegar, cocoa, and 3 Tbsp. braising liquid in a small bowl until smooth, then stir into braising liquid in pot. Bring to a simmer and cook, stirring occasionally, until sauce is slightly thickened and silky smooth, 5-10 minutes. Add pearl onions with cooking liquid and reserved bacon and mushrooms and cook until just heated through. Add chicken back to pot.
