Preheat the oven to 325°F (163°C).
Heat the vegetable oil in a large ovenproof casserole dish or Dutch oven over medium-high heat.
Add the beef cubes in batches, browning them on all sides. Remove the browned beef and set aside.
In the same dish, add the chopped onion, minced garlic, sliced carrots, and celery. Cook for 5 minutes until softened.
Sprinkle 2 tablespoons of flour over the vegetables and stir well to coat. Cook for 1 minute.
Return the beef to the dish. Stir in the beef broth, red wine, tomato paste, Worcestershire sauce, dried thyme, and bay leaves.
Season with salt and black pepper to taste. Bring to a simmer.
Cover the casserole with a lid or foil and transfer it to the preheated oven. Cook for 2 hours, or until the beef is tender.
While the beef cooks, prepare the dumpling dough by combining 1 1/2 cups all-purpose flour, baking powder, and 1/2 teaspoon salt in a bowl.
Add the whole milk and melted butter to the dry ingredients and stir until just combined. Do not overmix.
After 2 hours, remove the casserole from the oven and stir in the frozen peas.
Drop spoonfuls of the dumpling dough evenly over the surface of the casserole.
Return the casserole to the oven, uncovered, and bake for an additional 25 to 30 minutes until the dumplings are puffed and golden.
Remove bay leaves before serving. Serve hot.