PREPARATION
Prick bratwurst in several places with a knife and place in a large skillet. Add oil and half of beer, then add water until liquid comes a little over halfway up sides of sausages. Bring to a simmer over medium heat. Cook, turning once, until just barely cooked through, 12–15 minutes.
Increase heat to medium-high; cook until liquid is evaporated, 5–10 minutes. Roll sausages to edge of skillet and add onion to center. Cook, turning sausages often and stirring onion occasionally, until sausages are browned and onion is soft, 5–8 minutes. Transfer sausages to a plate.
Add cabbage and beet to skillet; season with salt and pepper. Cook, stirring often, until cabbage is wilted, about 5 minutes. Add vinegar, brown sugar, allspice, and remaining beer. Cover; cook until tender, 20–25 minutes. Serve sausages with cabbage mixture, topped with horseradish.