Brown the ground beef in a large pot over medium heat, breaking it up as it cooks. Once no pink remains, drain excess fat and set the beef aside.
In the same pot, add the sliced mushrooms and diced onion. Cook until the mushrooms release their liquid and the onion softens.
Stir in the minced garlic and cook for one minute. Sprinkle the flour and thyme over the mixture, stirring to coat everything evenly.
Slowly pour in the beef broth while stirring to avoid lumps. Return the ground beef to the pot.
Add the sliced carrots and green beans. Bring the stew to a gentle simmer and cook for 15 minutes, or until the carrots are tender.
Reduce the heat to low and stir in the heavy cream. Season with salt and pepper, then heat through without letting it boil.