Place a rack in lowest place of oven; preheat to 350°. Tie 1 small bunch thyme, 5 sprigs parsley, and 2 bay leaves along with kitchen twine; put aside. Sprinkle one 4-lb. piece untrimmed flat-cut beef brisket, extra fats trimmed, throughout with 4 tsp. Diamond Crystal or 2½ tsp. Morton kosher salt; season generously with freshly floor pepper.
Warmth 2 Tbsp. vegetable oil in a big Dutch oven or different heavy pot over medium-high. Cook dinner brisket till nicely browned, about 5 minutes per facet. Switch to a platter. Pour fats in pot right into a small bowl, then add 1 Tbsp. again to pot; set remaining fats apart.
Cook dinner 4 oz. bacon (about 4 slices), coarsely chopped, in similar pot, stirring sometimes, till browned and crisp, about 4 minutes. Utilizing a slotted spoon, switch bacon to a medium bowl. Pour off fats into bowl with reserved fats; add 2 Tbsp. again to pot.
Cook dinner 8 oz. crimini mushrooms, halved, quartered if giant, 1 giant carrot, peeled, coarsely chopped, 2 cups frozen pearl onions (from a 14.4-oz. bag), thawed, and 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt in pot, stirring sometimes, till greens are softened and browned, 6–8 minutes. Switch to bowl with bacon; put aside.
Add 2 Tbsp. fats to pot. Cook dinner 5 garlic cloves, smashed, stirring typically, 30 seconds. Stir in 2 Tbsp. all-purpose flour and prepare dinner, stirring consistently, 30 seconds. Add 2 Tbsp. tomato paste and prepare dinner, stirring typically, till barely darkened in shade, about 2 minutes. Pour in 3 cups dry pink wine, scraping up any browned bits caught to the underside of pot with a wood spoon. Convey to a boil and prepare dinner till wine is diminished by a 3rd, about 2 minutes. Take away from warmth and stir in 3½ cups low-sodium beef broth and remaining 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt. Fastidiously return brisket to pot, arranging fats facet up; tuck reserved herb bundle alongside.
Cowl pot and switch to oven. Braise brisket, spooning braising liquid over a couple of instances, 3½ hours. Uncover pot, take away and discard herb bundle, and stir in reserved bacon and greens. Return pot to oven and prepare dinner, uncovered, till brisket is deeply browned and really tender, 30–40 minutes. Let cool barely.
Switch brisket to a reducing board and slice in opposition to the grain. Skim fats from floor of braising liquid if wanted, then return brisket to pot. Prime with chopped parsley leaves simply earlier than serving.
Do Forward: Brisket Bourguignon (with out parsley) could be made 1 day forward. Let cool fully; cowl and chill. Reheat, lined, over medium warmth till brisket is warmed by means of, 12–18 minutes.