In a large bowl, toss the beef cubes with the flour, salt, and black pepper until evenly coated.
Heat the olive oil in a large, heavy-bottomed Dutch oven over medium-high heat. Sear the beef in batches until browned on all sides, then transfer to a plate.
Add the pearl onions and mushrooms to the pot. Sauté for 5 to 7 minutes until lightly browned and slightly softened.
Stir in the sun-dried tomatoes and pour in the beef broth, using a wooden spoon to scrape up any browned bits from the bottom of the pot.
Return the seared beef and any resting juices to the pot. Nestle the fresh rosemary sprigs into the broth.
Bring the stew to a boil, then immediately reduce the heat to low. Cover and simmer for 2 hours, or until the beef is completely tender.
Remove and discard the rosemary sprigs. Garnish the stew with freshly chopped parsley and serve warm.