Preheat a griddle or cast-iron skillet over medium-high. Place the celery and scallions in a bowl of ice water.
In a small skillet, heat the EVOO, five turns of the pan, over low to medium-low. Add the garlic in a single layer and cook until light golden, 3 to 5 minutes. Using a fork, transfer the garlic to a paper towel. Pour the EVOO into a small dish and let cool.
Pat the steaks dry, brush with the garlic-infused EVOO, then season with kosher salt, pepper and rosemary. Add the steaks to the hot griddle and cook, turning occasionally, to desired doneness, 10 minutes for medium-rare. Sear the edges; transfer to a cutting board and let rest 5 minutes. Slice the steaks crosswise against the grain. Douse with the juice of half a lemon; sprinkle with sea salt.
Drain the celery and scallions. Toss with the parsley, mushrooms, juice of 1 lemon, sea salt, pepper and cheese. Serve the steak with the salad.