Dissolve the sugar and yeast in the warm water in a measuring cup, let rest for 8 minutes.
In a separate bowl, combine the flour and salt. Pour yeast mixture over flour mixture. Add the olive oil, mix well.
Place the dough on a floured surface and knead for 2 minutes. You do NOT need to let this dough rise!! (Note: if you want to make extra dough to freeze and use later, roll the extra dough into a ball and place in a freezer bag and freeze. Thaw in the fridge completely and then begin with step four.)
Take two long pieces of tin foil and lay overlapping each other to make a large square. Spray with cooking spray. Roll dough in a large circle, about ½ inch thick and place on top of sprayed tin foil. Spray top of pizza dough with cooking spray. Holding each end of the foil, carefully place on the grill (with the foil on the bottom). Close grill lid. Cook for a couple minutes, until the bottom of the crust is how you like it. I like to rotate mine if I can because some spots in my grill get hotter than others.
Carefully take foil off the grill onto a heat resistant surface and flip dough over. Spread pesto on golden brown side of crust. Sprinkle feta cheese all over the pizza and then mozzarella. Top with sliced red onion and place back onto the grill. Half avocado and take out the pit. Place flat side down on the grill. After about 3-5 minutes, when the cheese is melted, open grill lid and take off avocado halves, slice and place onto pizza and close lid for about 1-2 minutes until heated through.
Take pizza off the grill and top with lots of diced basil leaves. Slice up and serve. Enjoy!!