Slice 2 large yellow onions into 1/4-inch half-moons and mince 2 cloves garlic.

Heat 1 tablespoon vegetable oil in a large skillet or Dutch oven over medium-high heat until shimmering, about 30 seconds.

Add 8 bratwurst sausages and brown on each side for 2 to 3 minutes until golden brown, then transfer to a plate.

Reduce heat to medium and melt 2 tablespoons butter in the same skillet until foaming.

Add sliced onions and cook, stirring occasionally, for 3 to 4 minutes until they soften.

Continue cooking onions, stirring every 2 to 3 minutes, for 10 to 12 minutes until deep golden brown, then add minced garlic and cook for 30 seconds until fragrant.

Pour 12-ounce beer into the skillet and scrape up browned bits, then stir in 1 teaspoon Dijon mustard and 1/2 teaspoon caraway seeds and cook for 1 minute.

Nestle browned sausages back into the skillet with any juices, ensuring liquid comes about halfway up the sausages.

Reduce heat to medium-low and simmer gently for 12 to 15 minutes, flipping sausages halfway through, until they reach 160°F internal temperature.

Remove skillet from heat and season the braising liquid with salt and pepper to taste.

Serve sausages in toasted buns topped with caramelized onions and a spoonful of the braising liquid.