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Preheat your oven to 350°F (175°C).
In a large oven-safe skillet or Dutch oven, heat the olive oil and butter over medium heat.
Add the sliced onions and cook, stirring occasionally, until they are soft and golden brown, about 20-25 minutes. This slow caramelization process brings out the natural sweetness of the onions.
Stir in the minced garlic and cook for another 2-3 minutes until fragrant.
Nestle the bratwursts among the onions in the skillet.
Pour the beer and beef broth into the skillet, ensuring the brats are mostly covered by the liquid. Stir in the Dijon mustard, and season with salt and pepper to taste.
Bring the mixture to a simmer on the stovetop, then transfer the skillet to the preheated oven.
Bake, uncovered, for 30-40 minutes, or until the bratwursts are cooked through and have absorbed the rich flavors of the braising liquid.
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