Place flour, salt, yeast, sugar and 1 Tbs. olive oil in food processor.  Add 1/2 cup warm water to moisten the yeast. Process mixture and drizzle more warm water through the feed tube until the mixture forms a ball.  Let process to knead the dough. Place dough into oiled bowl. cover with plastic wrap and keep in a warm place to rise for at least 30 minutes

While dough is rising, preheat grill to medium-high heat.   Slice zucchini, eggplant if using.  Keep red pepper whole and coat in 1 T olive oil, salt & pepper to taste.  Grill veggies just until grill marks appear.  Put aside in bowl.  Put red pepper in plastic bag and close to steam for 10+ minutes.  Once steamed, remove seeds & core and slice in strips.  Cut other veggies into strips.

Brush light coating of olive oil on grill pan.  Roll out dough on counter in a pool of flour. Lift pie onto grill pan and shape into place. Place toppings on pizza.  First 1 Tbs olive oil, then pesto, then veggies & tomatoes, then burrata cheese.  Place on medium-high grill and close lid. Turn heat down if necessary, so there is no flame below.  Check after 5 minutes and rotate pan for even grilling.  Pizza is done when crust is golden brown underneath and toppings look bubbly.  Use hot pads to remove pizza pan from grill.  Let pizza stand for 5 minutes. Remove from grill pan.  Spread arugula leaves over the pizza, cut and serve.