Preheat your grill to medium high and close the lid. Combine ingredients for rub and set aside. Mix together ingredients for glaze and set aside.
About 5 minutes before you are ready to grill, pat the rub all over the steak. Allow the beef to rest for about 5 minutes before grilling.
Pour a bit of vegetable oil onto a piece of paper towel and oil the grates of the grill. Place the steak on the grill and allow to cook with the lid open for 3 minutes. Flip the steak over and cook for another 3 minutes. Remove the steaks from the grill and place on a cutting board. Using a paper towel clean the grill of any spice clumps and reapply vegetable oil.
Liberally brush some glaze on one side of the beef and place the meat, glaze side down, onto the grill. Brush more glaze on the top of the steak and allow to cook for 2 minutes.
Turn the steak over and cook for an additional 2 minutes or until meat reaches an internal temperature of 145°F as measured with a food thermometer. Keep basting if you continue cooking.
Remove the meat from the grill and set it on a cutting board to rest for at least 5 minutes.
In the meantime, place the corn tortillas on a dish and cover with a damp paper towel. Heat the tortillas in the microwave for 30 seconds to 1 minute until heated through. Alternatively, if you do not have a microwave, lightly sprinkle each of the tortillas with water and wrap small batches (about 5) in foil. Heat on the grill for a few minutes. Place the tortillas on a dish and keep warm by placing a hot damp towel over them.
Chop the beef into bite sized pieces. Begin by slicing the meat into long strips against the grain and then cutting those strips crosswise into 1-inch pieces. If you have any remaining glaze, slather some of it onto the meat.
Set out platters and bowls containing the beef, the warmed corn tortillas, crumbled cheese, and radishes and lime wedges and allow your guests to help themselves.