Heat a large Dutch oven over medium-high heat. Add EVOO, 2 turns of the pan. Add coarsely chopped carrots, celery, onion and garlic. Tie thyme and rosemary together with kitchen twine and drop into pot along with bay leaves. Season with salt and toss peppercorns into pot. Cover and cook veggies 6-8 minutes, stirring occasionally until tender-crisp. Turn off heat and let cool.
While the vegetables cool, bring a few quarts of water to a boil, add pearl onions and boil 3 minutes. Drain and cool onions in an ice water bath. Trim at root end and squish the onions away from their skins. Place in baggie and throw in fridge.
Add wine and chicken to the pot with the veggies, pushing the pieces down so they are submerged in the wine. Place pot in fridge and chill overnight.
Remove chicken from wine and pat dry. Strain the wine and reserve it, discarding the marinade vegetables and herbs. Rinse and dry pot, place on stove over medium-high heat. Add a drizzle of EVOO to pot and the lardons. Brown and crisp the pork 5 minutes then remove and reserve.
Season the chicken with salt and pepper, brown in batches in the rendered fat until deep golden. Add another drizzle of EVOO if necessary for second batch.
Add reserved wine to pot and scrape up any drippings. Add stock and set chicken and pork back into pot. Add the chopped carrots and pearl onions. Bring to a boil then reduce heat and cook at a low boil for 20-25 minutes.
Remove chicken, onions and carrots to a platter, raise heat and thicken the reddish-brown liquid 6-8 minutes more until it becomes a thin, shiny gravy. In a small skillet, melt butter and whisk in flour. Cook 1 minute then whisk the butter-flour mixture into the Coq Au Vin sauce and let thicken, about 2-3 minutes.
Serve chicken, carrots and onions in shallow bowls topped with plenty of sauce.