Place the cut potatoes in a large stockpot, cover with cold water and add salt. Bring to a boil, then simmer until the potatoes are fork tender, about 20 to 30 minutes.
Drain well in a colander. While the potatoes are still warm, press them through a potato ricer or food mill and into a mixing bowl. Whip in the warm milk and softened butter until incorporated and the potatoes are fluffy. Cover and keep warm.
For the filling: In a 2-quart saucepan over medium heat, add the oil then braise the beef with the garlic, onion, and bay leaves. Season with salt and pepper. When the meat is browned and the onion is tender, dust with flour. Cook for 3 to 4 minutes, stirring often.
Pour in the beef broth and cook for 2 minutes until the mixture begins to thicken.
Add the canned tomatoes and the whole vegetables tied together. Simmer for 5 minutes to infuse the flavors, then remove the vegetable bundle.
Add the peas, carrots, pearl onions, and parsley. Taste and adjust seasoning as needed.
Transfer the meat mixture to a 9 by 13-inch casserole dish.
Spread the mashed potatoes evenly on top of the casserole. Dot with butter if desired.
Bake in a preheated 350 degree F oven until the potatoes are golden, about 30 minutes.
