Preheat the Oven: Initiate the preparation by preheating the oven to 350°F (175°C).
Prepare the Cooking Vessel: Utilize a large oven-safe skillet or Dutch oven. Place it on the stove over medium heat and combine the olive oil and butter, allowing the butter to melt and merge with the oil.
Caramelize the Onions: Introduce the thinly sliced onions to the skillet. Stir occasionally and allow them to cook until they achieve a soft and golden hue, approximately 20-25 minutes. This process is essential for developing the onions' inherent sweetness.
Incorporate Garlic: Add the minced garlic to the caramelized onions, stirring continuously, and cook for an additional 2-3 minutes until the aroma of the garlic is evident.
Add Bratwursts: Arrange the bratwurst sausages among the caramelized onions in the skillet, ensuring they are evenly spaced.
Prepare the Braising Liquid: Pour the beer and beef broth over the bratwursts and onions. Ensure that the liquid mostly covers the sausages. Stir in the Dijon mustard and season the mixture with salt and pepper according to taste.
Simmer and Transfer to Oven: Allow the contents of the skillet to come to a simmer. Subsequently, transfer the skillet to the preheated oven.
Bake: Let the dish bake, uncovered, for 30-40 minutes. The bratwursts should be thoroughly cooked and imbued with the flavors of the braising liquid.