Prepare your ingredients: Thinly slice red onions. Depending on how spicy you want your chimol to be, remove the seeds and membrane of the chiles, and thinly slice. Grate garlic. Slice radishes. Rough chop cilantro.
Mix together lime juice, red onion, chiles, garlic, radishes, and cilantro in a medium bowl. Season generously with salt and pepper. Stir in 1/4 cup olive oil. Let chimol sit at room temperature while the steak cooks.
Prepare a grill for medium-high heat. Oil grate with vegetable oil. Season steak with salt and pepper, and then rub all over with remaining tablespoon of olive oil. Grill, turning once, until deeply browned on the outside and cooked to desired doneness, 8-12 minutes for medium-rare. Transfer to a cutting board and generously drizzle with Worcestershire sauce. Let sit 5 minutes before thinly slicing.
Serve steak with chimol, warmed tortillas, and more Worcestershire sauce.