Pat beef cubes completely dry with paper towels, season generously on all sides with salt and pepper, and let rest at room temperature for 15–20 minutes.
Heat Dutch oven over medium heat, add diced bacon, and cook 8–10 minutes until crispy and fat is rendered. Transfer bacon to a paper towel-lined plate with a slotted spoon, leaving the fat in the pot.
Increase heat to medium-high; working in batches, sear beef in the bacon fat for 3–4 minutes per side until deeply browned, then transfer to a plate. Add olive oil between batches if needed — do not crowd the pot.
Reduce heat to medium, add 1 tbsp butter, then cook diced onion and carrots 5–6 minutes, scraping up the browned bits. Stir in garlic and tomato paste and cook 1–2 minutes until fragrant and the paste darkens.
Pour in the red wine, scraping up every bit of fond from the bottom, then boil vigorously for 5 minutes to reduce slightly and cook off the alcohol.
Return seared beef and any accumulated juices to the pot, add beef stock, bay leaves, and thyme, and bring to a gentle simmer — liquid should reach three-quarters up the beef. Season with salt and pepper.
Cover the Dutch oven and transfer to a preheated 325°F (165°C) oven; braise for 2.5–3 hours until beef is fork-tender, adding a splash of stock if liquid reduces too much.
About 30 minutes before beef is done, melt 1 tbsp butter in a skillet over medium heat and cook pearl onions 10–12 minutes until golden and caramelized, then set aside.
In the same skillet, melt remaining 1 tbsp butter and cook mushrooms undisturbed 3–4 minutes until browned, then stir and cook until all moisture evaporates and mushrooms are golden. Season lightly.
Remove pot from oven, discard bay leaves and thyme sprigs, then whisk flour into 1 cup of the braising liquid and stir the slurry back into the pot; simmer on stovetop 5–10 minutes until sauce coats the back of a spoon.
Gently stir in the reserved bacon, caramelized pearl onions, and sautéed mushrooms; heat through for 5 minutes, adjust seasoning, and garnish with fresh parsley before serving over mashed potatoes, egg noodles, or with crusty bread.