Preheat oven to 425°F and broiler to high, setting the rack 8 inches from the flame.
Put the steak on a broiler pan, drizzle with 1 tablespoon EVOO and season with salt and ground black pepper. Place under broiler for 15 minutes, turning once halfway through. Remove the meat from the broiler and let it to rest for 5 minutes, tented with a piece of aluminum foil.
Place the broccoli spears on a baking sheet and drizzle with EVOO. Top with crushed garlic cloves, salt and pepper. Roast in the oven for about 15 minutes.