Preheat oven to 425 degrees. Cut broccoli into large florets with some stalk attached. Toss with 2-3 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. For chimichurri, combine shallots, chiles, if using, garlic, vinegar and ½ teaspoon sea salt in a medium bowl.
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. Set the steak on a cutting board to rest.
Stir parsley into reserved chimichurri mixture. Using a fork, whisk in ½ a cup olive oil and season with more sea salt and pepper. Slice the steak against the grain into ¼-inch slices and serve with broccoli and chimichurri.