Bratwurst and Red Cabbage

Name: Bratwurst and Red Cabbage
Ingredients: 1 pound uncured bratwurst; 2 tablespoons olive oil; 1 12-oz. bottle Pilsner or other lager, divided; 1 medium red onion, chopped; ½ medium head of red cabbage, thinly sliced; 1 medium red beet, peeled, coarsely grated; Kosher salt and freshly ground black pepper; ½ cup apple cider vinegar; 1 tablespoon light brown sugar; ¼ teaspoon ground allspice; Freshly grated horseradish (for serving)