Score both sides of steak in a diamond pattern by carefully making 1/8-inch-deep diagonal cuts with a sharp knife at 1" intervals. Rub half of the garlic and 2 teaspoons of the rosemary into both sides of meat and season with salt and pepper.
Heat 1 tablespoon of the oil in a large nonstick skillet over medium-high heat. Add steak and cook, turning once, about 4 minutes per side for medium-rare. Transfer to a plate and loosely cover with foil to keep warm.
Heat remaining oil in the same skillet. Add onion and cook, stirring often, for 2 minutes. Add remaining garlic and cook, stirring constantly, until fragrant, about 30 seconds. Add asparagus and mushrooms and cook, stirring often, until asparagus is crisp-tender and almost all the liquid has evaporated, about 5 minutes. Stir in lemon zest and remaining rosemary; season to taste with salt and pepper.
Cut steak into thin slices and serve with the vegetables.