In a large saucepan, melt the butter over medium heat.
Once heated, add the sausages and cook until golden brown on each side. Do not cook through. Once golden, remove to a plate and set aside.
Reduce heat to medium low and add the sliced onions. If needed, add a little more butter. Cook, stirring occasionally, until golden brown and caramelized. Adjust heat between medium and low as needed to caramelize the onions without burning.
Add the garlic and cook just until fragrant, 30 seconds to 1 minute.
Stir in the fresh thyme, salt, paprika, and black pepper.
Pour in the beer, scraping any browned pieces that have stuck to the bottom of the pan.
Gently add the sausages back into the pan with the beer. Increase heat to medium.
Bring the mixture to a simmer and cook until the sausages are cooked through and the beer has reduced, about 15 minutes.
Slice the hoagie or hot dog buns in half lengthwise if not precut. Spread the mustard on one inner side.
Add a bratwurst and top with caramelized onions and shredded cheese. Repeat with remaining ingredients to make four sandwiches.
Arrange the sandwiches on a baking sheet and place under the broiler. Cook until the cheese is melted and bubbly.
Serve immediately.