Step 1

Heat broiler. Brush a rimmed baking sheet with oil and arrange slices in a single layer; brush 1 teaspoon oil over tops. Broil 4 inches from heat, without turning, until golden and browning in spots, 20 to 25 minutes.

Step 2

Meanwhile, season steak with salt. In a large skillet, heat oil over high and swirl to coat. In batches, cook steak, undisturbed, until brown on one side, 2 minutes (do not crowd pan). Flip and cook until cooked just cooked through, 1 minute. Transfer to a plate.

Step 3

Add broccoli and 1/3 cup water to skillet and cook until broccoli is bright green and water almost evaporates, about 2 minutes. Add garlic and rosemary and cook, stirring, until fragrant, 15 seconds. Add vinegar and bring to a boil. Remove from heat, return steak to skillet and toss to coat. Add butter and swirl until melted. Season with salt. Serve over polenta slices.