Place the butter in a bowl and set aside to soften. Place an oven rack in the center of the oven, then preheat to 450°F. Wash and dry the fresh produce.

Halve the potatoes lengthwise; cut crosswise into ½-inch pieces. Cut off and discard the bottom 1/2 inch of the broccoli stem; cut the broccoli into small pieces, keeping the florets intact. Quarter and deseed the lemon.

Line a sheet pan with aluminum foil. Place the sliced potatoes and broccoli pieces on the foil. Drizzle with olive oil and season with salt and pepper; toss to coat. Arrange in an even layer.

Roast, rotating the sheet pan halfway through, 25 to 27 minutes, or until browned and tender when pierced with a fork. Remove from the oven. Evenly top with the juice of 2 lemon wedges; season with salt and pepper to taste.

Once the vegetables have roasted for about 10 minutes, pat the steaks dry with paper towels; season with salt and pepper on both sides. In a medium pan, heat 2 teaspoons of olive oil on medium-high until hot. Add the seasoned steaks and cook, turning occasionally. Transfer to a cutting board and let rest for at least 5 minutes.

While the steaks cook, to the bowl of softened butter, add as much of the chile paste as you’d like, depending on how spicy you’d like the dish to be. Stir to thoroughly combine.

Find the lines of muscle (or grain) on the rested steaks; thinly slice crosswise against the grain. Serve the sliced steaks and roasted vegetables with the remaining lemon wedges on the side. Top the steaks with the chile butter. Garnish the vegetables with the cheese.