Heat a Dutch oven over medium-high heat. Add the beef cubes and cook until browned on all sides, about 6 minutes. Remove the beef to a plate and set aside.
Lower the heat to medium. Add the butter, then the sliced mushrooms and pearl onions. Cook until the mushrooms release their liquid and begin to brown, about 5 minutes.
Stir in the minced garlic and thyme and cook for 1 minute until fragrant.
Sprinkle the flour over the vegetables and stir for 1 minute to form a roux.
Slowly pour in the beef broth while stirring to avoid lumps. Return the browned beef to the pot along with the salt and pepper.
Bring the stew to a simmer, then reduce heat to low, cover, and cook for 1 hour until the beef is tender.
Remove the pot from the heat. Stir in the Greek yogurt until fully combined and the broth looks creamy. Taste and adjust salt if needed.
Ladle into bowls and top with chopped parsley before serving.