This classic French recipe is executed simply and easily here. Don't worry if you can't find veal stock — go ahead and use chicken stock instead. However, veal stock does add a complexity and body to the flavor of the sauce that can have guests searching for that "je ne sais quoi."
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Place the garlic, thyme, bay leaves, and peppercorns into a cheesecloth and tie like a tea bag with some kitchen twine. Dredge the chicken drumsticks and thighs in the flour, shaking off excess flour.
Heat a very large pot filled with enough oil to cover the bottom of the pan. Fry all of the chicken until golden on the outside, but still raw in the middle. Carefully drain off all oil from the pan but do not wash out the pan.
Add the onions and carrots to the pan and sweat for 1-2 minutes over low heat. Add the crisped chicken to the pan and deglaze with the wine. Add the veal stock and chicken stock, bring up to a simmer and cook until the chicken is so tender that it can be eaten with a spoon, roughly 2-3 hours.