6 cups shredded (from half a 2-pound cabbage) red cabbage
Coarse salt and ground pepper
1 tube (18 ounces) prepared plain polenta
1 tablespoon chili powder
1 tablespoon sugar
1 1/2 pounds flank steak
Heat broiler; set rack 4 inches from heat. In a large bowl, whisk vinegar and 3 teaspoons oil; add cabbage. Season with salt and pepper; toss to combine. Set aside.
Cut polenta crosswise into 8 equal slices. Heat 1/4 cup oil in a large nonstick skillet over medium heat; add polenta slices and cook until golden on both sides, about 10 minutes per side. Transfer to a paper-towel-lined plate; season with salt.
Combine chili powder, sugar, 1 teaspoon salt, and 1/4 teaspoon pepper. Place steak on a broiler-proof pan. Coat both sides with remaining teaspoon oil and spice mixture. Broil (without turning) about 10 minutes for medium-rare; let rest 5 minutes. Slice thinly; serve with cabbage salad and polenta rounds.
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