Preheat the oven to 400°F. Coat potatoes lightly with olive oil and sprinkle generously with salt and pepper. Bake for 1 hour, or until easily pierced with a fork. Set aside until cool enough to handle. Switch the oven to Broil.
Slice each potato lengthwise across the top, leaving enough of the skin intact to hold the filling. Scoop out the insides and transfer them to a mixing bowl.
Set a medium skillet over medium-high heat. Add the sliced bratwurst in an even layer. Cook 3–5 minutes per side, until browned. Transfer to a cutting board and chop into small pieces. Do not wipe out the skillet.
Lower the heat to medium. Add sliced onions to the skillet and season with salt and pepper. Cook, stirring often, about 20 minutes, until deep golden brown.
Add chopped bratwurst and lager to the skillet. Stir as the beer reduces slightly. Adjust seasoning as needed.
Add butter, mozzarella, and the bratwurst-onion mixture to the bowl with the potato insides. Stir gently to combine and season to taste.
Spoon the filling generously into the potato shells. Place on a baking sheet and broil 1–2 minutes, just until the tops begin to brown.
Top each potato with sauerkraut and a little black pepper. Serve warm.