Preheat the oven to 250 degrees F.
Heat the olive oil in a large Dutch oven over medium-high heat. Add the beef cubes in batches, seasoning each with salt and pepper, and sear until browned on all sides, about 3 to 5 minutes per batch. Transfer the browned beef to a large plate and set aside.
In the same Dutch oven with the browned bits, add the sliced onions and season with salt and pepper. Cook until the onions are soft and translucent, approximately 5 minutes. Add the carrots and garlic, cooking for 30 seconds to 1 minute. Pour in 1 cup of beef broth and increase the heat to high, allowing the liquid to reduce by half, about 5 minutes.
Return the beef and any accumulated juices to the Dutch oven. Add the remaining 2 cups of beef broth, tomato paste, thyme, and bay leaves. Bring the mixture to a simmer over high heat. Remove from heat, then stir in 1 cup of cranberries. Cover with a tight-fitting lid and transfer the pot to the oven. Cook for 2 hours or until the meat is tender and easily shreds with a fork.
Remove the pot from the oven and place it over medium heat on the stove. In a small bowl, combine 2 tablespoons of butter and the flour to form a smooth paste. Stir this paste into the stew. Add the remaining 1 cup of cranberries and cook until the stew thickens just slightly.
Meanwhile, melt the remaining 2 tablespoons of butter in a large skillet over high heat. Add the sliced mushrooms and season with salt and pepper. Cook until the mushrooms are browned and caramelized, about 5 minutes. Stir the mushrooms into the stew and simmer for another 10 minutes. Taste and adjust seasoning with salt and pepper as needed before serving.