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For the corned beef: Preheat the oven to 325°.
Unwrap the brisket and place it fat side up inside a baking dish. If it came with a spice packet, sprinkle it over the top, then sprinkle on the black pepper and rub it in. Cover the dish with heavy aluminum foil and place it in the oven for 2 1/2 hours, then uncover and continue baking for 30 to 45 minutes.
Check the brisket by inserting a fork in the meat. If it goes in easily, it’s ready; if it meets with resistance, bake for another 30 minutes—or up to an hour in some cases! If the brisket is tough, it hasn't cooked long enough! Once the brisket is fork-tender, remove it from the oven and let it rest, covered loosely in foil.
While the brisket is resting, make the balsamic reduction: Combine the balsamic and the sugar in a small saucepan over medium-high heat. Stir it together and bring the mixture to a boil, then reduce to medium-low and simmer until the mixture is thick and reduced by half. Set it aside.
Next, make the cabbage: Raise the oven temperature to 350 degrees. Cut the cabbage into 8 wedges. Heat the olive oil in a large, heavy skillet over medium-high heat and add the cabbage. Sear it on both sides until the cabbage gets as much color as possible, about 1 minute per side. Use a spatula to transfer the cabbage to a rack placed over a rimmed baking sheet. Sprinkle the cabbage pieces with salt and pepper. Pour the Guinness into the bottom of the baking sheet, then carefully transfer the pan to the oven. (The beer will gently steam the cabbage and infuse it with stouty essence). Bake the cabbage for 20 minutes, or until tender and deeper brown.
To serve: Slice or shred the rested beef on a cutting board (it should be very, very tender and almost falling apart). Then place it on a large platter alongside the cabbage wedges. Drizzle generous spoonfuls of the balsamic reduction all over the cabbage slices.