For the crust, stir all ingredients together, except flour. Add flour, stir until you can’t anymore, then knead for a bit by hand. Add a little more flour, as necessary, until dough is still slightly tacky to the touch, but not too sticky to manage. No raising necessary.
*Make sure to have all your ingredients ready and within reach before starting to grill.
Heat grill to high heat. Season chicken, pepper and onion pieces well with an all-purpose seasoning (I used Greek seasoning). Melt about 1 Tbsp. butter butter on a grill mat and spread around. Grill your chicken, bell pepper and onion pieces together on the grill mat, flipping and moving them around often, until chicken is cooked all the way through and peppers and onions are tender. If you don't have a grill mat, you can use a cast iron skillet over the grill too. Remove chicken fajita mixture to a bowl, once done, and set aside.
Next, form dough rounds by breaking off a fistful of dough and rolling it out flat on a floured surface. Brush olive oil on one side of your dough rounds and place them oil side down on the grill. Brush oil on the dough that's facing up, while letting that grill for about 1-2 minutes, then flip. Now put your toppings on the grilled side. Spread on some chunky salsa, sprinkle with cheese and the chicken fajita mixture, then more cheese and let that grill until the under side of the crust is done, about another 1-2 minutes. Check it by slightly lifting a side with a metal spatula and making sure there are nice, pronounced grilled marks. Close the grill hood for this part so the cheese can melt and everything can warm through. Serve immediately.