1. Adjust an oven rack to the lower-middle position and heat the oven to 300 degrees. Dry the beef thoroughly with paper towels, then season it generously with salt and pepper to taste. Heat 1 tablespoon of the oil in a large ovenproof Dutch oven over medium-high heat until shimmering. Add half of the meat so that the individual pieces are close together but nt touching. Cook, not moving the pieces until the sides touching the pot are well browned, 2 to 3 minutes. Using tongs, turn each piece and continue cooking until most sides are well browned, about 5 minutes longer. Transfer the beef to a medium bowl, add another 1 tablespoon of the oil to the pot, and swirl to coat the pan bottom. Brown the remaining beef; transfer the meat to the bowl and set aside.
2. Reduce the heat to medium, add the remaining 1 tablespoon oil to the now-empty Dutch oven, and swirl to coat the pan bottom. Add the onions and 1/4 teaspoon salt. Cook, stirring frequently and vigorously , scraping the pot bottom with a wooden spoon to loosen the browned bits, until the onions have softened, 4 to 5 minutes. Add the garlic and continue to cook for 30 seconds. Stir in the flour and cook until lightly colored, 1 to 2 minutes. Add the wine, scraping up the remaining browned bits from the bottom and edges of the pot and stirring until the liquid is thick. Gradually add the broth, stirring constantly and craping the pan edges to dissolve the flour. Add the bay leaves and thyme and bring to a simmer. Add the meat and return to a simmer. Cover and place the pot in the oven. Cook for 1 hour.
3. Remove the pot from the oven and add the potatoes and carrots. Cover and return the pot to the oven. Cook until the meat is just tender, about 1 hour. Remove the pot from the oven. (The stew can be covered and refrigerated for up to 3 days. Bring to a simmer over medium-low heat.)
4. Add the peas, cover, and allow to stand for 5 minutes. Stir in the parsley, discard the bay leaves, adjust the seasoning, and server immediately.