Step 1

Toss zucchini, vinegar, chopped oregano, and ¼ cup oil in a medium bowl to combine; season zucchini salsa with salt and pepper. Set aside.

Step 2

Prepare a grill for high heat. Meanwhile, flatten your steak. Cover a cutting board with a long piece of plastic wrap and set steak on top; fold plastic over steak to cover. Using the smooth side of a meat mallet, pound steak to about ½" thick. (Don’t hold back; you want it good and roughed up.) Pat steak dry with paper towels; season generously with salt and rub a bit of oil all over. Grill until browned, about 2 minutes per side for medium-rare. (You might not get that much color on this steak because it’s so thin, but you don’t want it to be overcooked.) Transfer steak to a cutting board and let rest 5–10 minutes. Cut in half lengthwise with the grain, then slice thinly against the grain.

Step 3

Arrange steak on a platter and spoon half of reserved salsa along with some juices over steak. Top with oregano leaves. Serve remaining salsa alongside.

Step 4

Do Ahead: Zucchini salsa can be made 1 day ahead. Cover and chill.