Bratwurst and Red Cabbage

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.