Pat the beef dry and toss it with the flour, salt, and pepper until evenly coated.
Heat the oil in a Dutch oven over medium heat. Brown the beef in two batches, then set it aside on a plate.
Add the onion to the same pot and cook until it softens. Stir in the garlic and cook for one minute more.
Add the mushrooms and cook until they start to release their liquid and brown slightly.
Pour in the ale and scrape the bottom of the pot to loosen any browned bits.
Return the beef to the pot along with the beef broth, carrots, and thyme sprigs.
Bring the mixture to a simmer, then cover and transfer to a 325°F oven. Cook for 2 hours until the beef is tender.
Remove the thyme stems before serving.