To make pesto, in food processor, combine arugula, basil, Parmesan, pine nuts, garlic, salt and pepper. With the motor running, gradually pour in ¼ cup (60 mL) of the olive oil and blend until smooth, scraping down the food processor as needed. (Pesto can be made up to 3 days ahead; refrigerate in an airtight container with a little extra olive oil added to cover the surface.)
Roll pizza dough into rough oval shape, ¼ -in. (5-mm) thick. Brush both sides of dough with 1 tbsp (15 mL) olive oil. Place bowls of mozzarella, tomatoes and ½ cup (125 mL) of the pesto near the grill.
Place pizza dough on grill preheated to high. Grill 1 to 2 min., until dough is lightly browned on bottom, turn over. Quickly spread pesto on pizza crust, top with mozzarella and tomato slices. Close lid and cook until dough is fully cooked and golden brown, 2 to 3 min. Cool 2 to 3 min. before slicing.
Substitute equal parts spinach, kale, parsley or a mixture of greens for the arugula. Leftover pesto can be tossed with pasta, spread on toast or stirred into soups.