Begin by cutting your chuck beef into 4-5 cm (2-inch) cubes. Season the beef generously with salt and pepper.
In a large Dutch oven, heat 2 tablespoons of olive oil over medium-high heat. Add the seasoned beef cubes in batches and sear each side until browned, about 3-4 minutes per side. Remove and set aside.
In the same pot, add another tablespoon of oil if needed and toss in the sliced carrots and pearl onions. Cook for about 5 minutes until they start to soften.
Add minced garlic, bay leaf, thyme sprigs, and tomato paste to the vegetable mixture. Stir well and let cook for another 2 minutes until fragrant.
Pour in 750ml of apple vinegar to deglaze the pot, scraping up any bits stuck to the bottom. Allow it to simmer for about 5 minutes.
Return the seared beef back to the pot along with any accumulated juices. Sprinkle flour over everything and stir well. Slowly pour in beef stock while stirring continuously.
Bring everything to a gentle simmer, cover with a lid, and reduce heat to low. Let it cook for about two hours, stirring occasionally.