Start your charcoal or gas grill, (on low heat). Spread the charcoal evenly on the bottom of the grill. Cook the veggies and mushrooms in a grilling pan until slightly charred. Alternatively, saute the veggies on the stovetop in a dry, cast iron skillet until softened and slightly charred.
Once the coals have cooled to where you can place your hand over them for 4 or 5 seconds, oil one side of the naan and place on the grill, oiled side down. After about a minute and the naan is lightly charred, turn, oil again and place the cheese on first then the toppings. Cover the grill. In 1 1/2 to 3 minutes the cheese has started to melt and the naan will have a good crispy char on the bottom.
Remove from the grill with a couple pancake turners, (with some help), top with chopped basil, red pepper flakes or extra cheese if desired. Serve right away.
Notes
Nutrition information is for 1 whole pizza. The toppings indicated are what I used. You can use any topping you like.When I made the pizzas the charcoal was still a little too hot. Make sure you let them cool down before you throw on the naan. Mine tasted great, but the cheese could have melted a little more. If you smell bread burning you know that they are ready to take off the grill!