Dissolve yeast in warm water in a large bowl; let stand for 5 minutes. Stir in 1 1/2 teaspoons oil. Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, sugar, salt, oregano, and thyme. Add to yeast mixture; stir well. Turn dough out onto a lightly floured surface. Knead until smooth and elastic (about 10 minutes).
Place dough in a large bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 45 minutes or until doubled in size. (Press two fingers into the dough. If indentation remains, the dough has risen enough.) Punch dough down; cover and let rest 5 minutes. Divide in half. Roll each half into a 9-inch circle on a floured surface.
Heat a grill pan coated with cooking spray over medium heat. Place one dough portion on pan; cook 10 minutes. Turn dough over; sprinkle with 1/4 cup mozzarella and 2 tablespoons Parmesan. Cook 10 minutes; remove from pan. Repeat procedure with remaining dough and cheeses.
Combine 2 teaspoons oil, arugula, and remaining ingredients in a medium bowl. Spoon 2 cups salad onto each pizza crust using a slotted spoon. Cut each pizza into 4 wedges. Serve immediately.