Preheat oven to 350°F.
In a large oven-safe skillet or Dutch oven, heat olive oil and butter over medium heat.
Add onions and cook for 20–25 minutes, stirring occasionally, until golden and soft.
Stir in garlic and cook for another 2 minutes.
Nestle the brats among the onions. Pour in beer and beef broth.
Stir in Dijon mustard. Season with salt and pepper.
Bring to a light simmer, then transfer the skillet to the oven.
Bake uncovered for 30–40 minutes, until the brats are cooked through and infused with flavor.
Serve warm with the onions spooned over top.