Start on the Quick-Pickled Cukes first, so they soak in flavor.
Preheat grill to 350° to 400° (medium-high) heat. Rub steak with olive oil and desired amount of salt and pepper. Let stand 10 minutes. Grill, covered, 5 minutes on each side or to desired doneness. Let stand 10 minutes.
Meanwhile, sauté garlic in hot sesame oil in a saucepan over medium heat 1 minute. Stir in soy sauce, next 3 ingredients, and 1/4 cup water; bring to a boil. Whisk together cornstarch and 1 tsp. water, and stir into soy sauce mixture. Bring to a boil; boil, stirring often, 1 minute.
Cut steak across the grain into thin strips. Arrange Quick-Pickled Cukes on a platter, and top with sliced steak and sauce.