4 chicken legs (thigh and drumstick)
Kosher salt, freshly ground pepper
2 cups dry white wine
1 bunch thyme, divided
4 oz. thick-cut bacon, cut crosswise into ¾" pieces
8 oz. shiitake mushrooms, stems removed, caps torn into 3 pieces
4 Tbsp. unsalted butter, divided
8 oz. carrots, peeled, cut crosswise into 4" pieces
4 shallots, peeled
2 garlic cloves, smashed
2 Tbsp. white wine vinegar
1 Tbsp. all-purpose flour
Handful of chopped parsley
Pat chicken dry with paper towels; season aggressively with salt and pepper. Transfer chicken to a 1-gallon resealable bag or an 8x8" glass baking dish. Pour wine over, then add ½ bunch thyme. Turn to coat, seal bag or cover baking dish, and let sit at room temperature while you prep the other ingredients. (Or, chill up to 48 hours.)
Cook bacon in a 10" or 12" nonstick skillet, preferably not cast iron, over medium heat, stirring occasionally, until brown and crisp but all of the fat hasn’t rendered out, 8–10 minutes. Transfer to a plate with a slotted spoon. (Medium heat lets you work in batches without having to worry about scorching your pan, and you’ll eventually use all the browned bits to build a deeply flavored braising liquid.)
Add mushrooms to bacon drippings in pan; season with salt. Cook, tossing occasionally, until tender and golden brown but not crisp, about 6 minutes. Scrape mushrooms into Instant Pot insert and reserve pan.
Meanwhile, remove chicken from marinade and place on a large plate; reserve marinade but pluck out and discard thyme sprigs. Pat chicken skin dry with paper towels. Heat 2 Tbsp. butter in reserved pan over medium. If you’re using a 10" skillet, you’ll have to do this in 2 batches, but chicken should all fit in a larger pan. As soon as butter is foaming, add chicken, placing skin side down, and cook, undisturbed, until skin is dark golden brown and plenty of fat is cooked out, 10–12 minutes. Turn onto flesh side and cook until pale golden brown underneath, about 2 minutes. Nestle chicken into pot insert.
Pour off all but about 1 Tbsp. accumulated drippings in pan (save it—this is a cross between clarified butter and schmaltz and can be used to sauté or roast basically anything). Add carrots, shallots, and garlic; season lightly with salt. Cook, tossing often, until shallots are golden brown in spots, about 4 minutes. Add to pot insert along with half of the reserved bacon.
Return pan to medium heat and pour in vinegar. Cook, scraping up browned bits with a wooden spoon, until syrupy, about 3 minutes. Add reserved wine marinade and remaining ½ bunch thyme and bring to a simmer. Cook, stirring and scraping bottom of pan, until reduced by half, 5–7 minutes.
Pour liquid over chicken and seal pot. Set for “Pressure Cook,” high, 15 minutes. Let natural release 10 minutes, then unseal.
Meanwhile, smash flour and remaining 2 Tbsp. butter together with a fork in a small bowl until well combined.
Transfer chicken legs and vegetables to a platter or plates. Pluck out and discard thyme sprigs from liquid. Add butter-flour mixture to liquid and whisk to melt. Bring to a simmer on high “Sauté” setting and cook to thicken sauce, about 3 minutes. Taste and adjust seasoning, if needed. Stir in parsley.
Serve coq au vin with braising liquid poured over and all around. Sprinkle remaining reserved bacon over.