In a heavy-bottomed oven-safe pan or large skillet set over medium heat, add the beef, pork, veal, and diced onions. Cook until meat is cooked completely, crumbling the meat as it cooks. Drain the excess grease.
Stir in the garlic and tomato paste and cook for 1-2 minutes. Add the beer, Worcestershire sauce, brown sugar, thyme, salt, and pepper. Reduce heat to medium-low. Cover and simmer for one hour.
Meanwhile, peel the potatoes and cut them into one-inch cubes. Add to a pot of water and bring to a boil. Simmer until potatoes are fork-tender, approx. 15 minutes. Drain.
While the potatoes cook, add the butter and cream to a small saucepan and warm gently until butter is melted.
After draining the potatoes, add the cream cheese to the hot pot. Using a potato ricer, rice the potatoes, adding them back into the same pot. (The hot potatoes will melt the cream cheese.)
Pour in the warm cream mixture and stir to incorporate with the riced potatoes. Fold in the shredded cheese and season to taste with salt and pepper.
Preheat the oven to 400 degrees.
If necessary, transfer the meat mixture to an oven-safe skillet.
Top the meat mixture with the mashed potatoes, spreading into an even layer. Cover with foil and bake for 20 minutes. Turn the oven to broil. Remove the foil and broil for 3-4 minutes until golden on top.