Heat broiler, with rack 4 inches from heat. Line a rimmed baking sheet with aluminum foil; set aside. In a medium bowl, gently stir together avocado, radishes, cilantro, jalapeno, lime juice, and oil; season with salt. Cover with plastic wrap, pressing it directly against surface of salsa (to prevent discoloring); set aside.
Arrange steak on prepared baking sheet. Rub both sides with cumin; season generously with salt and pepper. Broil without turning until well browned, 6 to 8 minutes for medium-rare. Transfer steak to a cutting board; tent with foil, and let rest 5 minutes.
While the steak is broiling, stack and wrap tortillas in a dampened kitchen towel; microwave until hot and pliable, 1 to 2 minutes. (Alternatively, wrap in foil, and warm in oven in lower third, 5 minutes.)
Cut steak crosswise into 2-inch-wide pieces; slice thinly on the diagonal. Dividing evenly, place beef on tortillas; top with salsa. Serve with lime wedges, if desired.