Slice the rested steaks into very thin strips. Using a sharp, straight-edge knife works best, rather than a serrated knife.
Assemble all the ingredients in little bowls to take out to the grill: sauce, peppers, tomato, mushrooms, steak, cheese, herbs.
Roll out the pizza dough. Put on the grill (using a rolling pin helps for transport of the dough to the grill) and cook a minute or so until lightly browned on the under side.
Flip the dough, and, working quickly, add the toppings in the following order: sauce, peppers, tomato, mushrooms, steak, cheese, herbs.
Close grill and cook 2-4 minutes until crust is crisp, cheese is melted, and toppings are heated through. Serve.