Preheat oven to 350 degrees and grease a large 9x13 casserole dish.
In a large pan, brown ground beef and crumble. Cook to lightly browned while crumbling, do not burn. Do not drain fat.
Remove ground beef from pan and set aside. Add onions, celery, and carrots, to pan and saute until lightly browned, about 8 minutes, stirring occasionally.
Stir in garlic, Montreal steak seasoning, browned ground beef, and pub cheese. Stir in butter and stock.
Cook, stirring often, until pub cheese and butter are melted and well incorporated.
Spread out stale cubed hamburger buns in casserole pan.
Pour hamburger, stock, and vegetable mixture over buns, stir to mix.
Bake 45-60 minutes until bubbly and golden brown - there should be a little liquid left in the pan but not much - do not cook all the liquid off, as it will re-absorb into the stuffing as it cools (think just a tiny amount on the bottom of the pan.)