Heat 1 tablespoon vegetable oil in a large heavy skillet over medium-high heat. Add the bratwurst and cook until browned, about 3-4 minutes per side. Remove from the pan and set aside on a plate.
Add the remaining 1 tablespoon vegetable oil to the skillet along with the thinly sliced white onion. Season with 1/2 teaspoon salt and 1/2 teaspoon black pepper. Cook for 7-8 minutes until the onions soften and turn golden, stirring frequently.
Stir in 1 tablespoon minced garlic and cook for one minute.
Pour in 12 ounces beer and return the bratwurst to the skillet. Bring the beer to a simmer, then reduce heat to medium-low. Simmer for 8-10 minutes until the onion mixture thickens and the bratwurst are fully cooked to an internal temperature of 165 degrees Fahrenheit.
Serve the bratwurst on toasted buns, drizzled with stone-ground mustard.