Preheat the oven to 325°F (163°C).
Pat the beef cubes dry with paper towels and season generously with salt and black pepper.
Heat the vegetable oil in a large oven-safe casserole dish or Dutch oven over medium-high heat.
Add the beef in batches, browning all sides for about 5 minutes per batch. Remove browned beef and set aside.
In the same dish, add the chopped onion and cook for 3-4 minutes until softened.
Add the minced garlic, sliced carrots, and celery; cook for another 3 minutes, stirring occasionally.
Sprinkle the 2 tablespoons of flour over the vegetables and stir well to coat. Cook for 1 minute to remove raw flour taste.
Return the browned beef to the dish. Stir in the tomato paste, dried thyme, dried rosemary, and bay leaves.
Pour in the beef broth and red wine, scraping the bottom of the dish to loosen any browned bits.
Bring the mixture to a simmer on the stovetop.
Cover the casserole with a lid or foil and transfer to the preheated oven.
Bake for 2 hours, or until the beef is very tender.
While the casserole cooks, prepare the dumpling dough: In a medium bowl, whisk together 1 1/2 cups flour, baking powder, and salt.
Add the milk and melted butter to the dry ingredients and stir just until combined. Do not overmix.
After 2 hours of baking, remove the casserole from the oven and discard the bay leaves.
Drop spoonfuls of the dumpling dough evenly over the surface of the casserole stew.
Return the casserole uncovered to the oven and bake for an additional 25-30 minutes, or until the dumplings are puffed and golden on top.
Remove from the oven and sprinkle chopped fresh parsley over the top before serving.