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Preheat oven to 425 degrees. Cut broccoli into large florets with some stalk attached. Toss with 1-2 tablespoons of olive oil and season with sea salt and pepper. Spread on a baking sheet and roast, tossing and rotating halfway through, until crisp around the edges and charred in spots, 35–40 minutes.
Meanwhile, season steak generously with sea salt and let sit. Heat a dry large skillet over medium-high. Swirl oil in pan to coat. Pat steaks dry and cook for 3-5 minutes per side until cooked to your desired level of doneness. 2 Minutes before done add in the butter and baste steak with the butter. Set the steak on a cutting board to rest.
Slice the steak against the grain into ¼-inch slices and serve with broccoli and chimichurri.