Prepare the patties: Preheat the griddle to low heat. Use a sharp knife to remove the casings from the sausage links. Shape the sausage into 7 small patties. Transfer to a plate and set aside.
Prepare the beer cheese sauce: Preheat a medium saucepan on the griddle. Once hot, remove the pan from the heat and add the beer and garlic. Stir until well combined. Add the heavy cream and mustard, then return the pan to the hot griddle. Cook, stirring occasionally, until the sauce just starts to bubble.
Stir in the cheese until melted. Add more cheese, if needed, to make the sauce thicker, until the sauce sticks the back of the spoon but still runs off the spoon.
Cook the peppers and onions: Melt the tallow on the hot griddle. Add the peppers and onions to the griddle and sprinkle with the all purpose seasoning. Cook for 5 to 7 minutes, stirring occasionally, until slightly charred.
Cook the burgers: Add the burger patties to the hot skillet and cook until they develop a nice crust on the bottom. Flip and cook the patties until they reach an internal temperature of 165°F on an instant-read thermometer inserted into the thickest part of the burgers.
Toast the buns: Add the tops and bottoms of the buns to the griddle and cook until toasted.
Assemble: Spread a small amount of mustard on the bottom of the buns, to taste. Dividing evenly among the bottom of the buns, top with the burgers, then the peppers and onions. Drizzle the beer cheese over the top and finish with the tops of the buns. Serve immediately.