Heat oven to 350°F. Soak tomatoes in boiling water in a small heat-proof bowl 5 minutes. Drain.
Spread one cutlet between 2 sheets of parchment or waxed paper. Pound slightly to even 1/8-inch thickness. Repeat with remaining cutlets, Season cutlets with Italian seasoning and a total of 1/4 teaspoon salt and 1/8 teaspoon pepper.
Place 2 to 3 arugula leaves onto each cutlet. Top each with 3 softened tomatoes and 1 tablespoon mozzarella. Starting at a short end, roll up each cutlet. Secure with toothpicks.
Coat 12-inch nonstick skillet with cooking spray. Heat over medium-high heat. Add roll-ups; cook until evenly browned, about 3 minutes. Transfer to ungreased baking dish large enough to hold them in one layer.
Bake in 350°F oven until cooked through, 15 to 20 minutes. Remove from oven; let stand 5 minutes.
Meanwhile, cook noodles in large pot of salted boiling water, following package directions, about 10 minutes.
While noodles are cooking, coat skillet with more spray. Heat over medium-high heat. Add shredded zucchini and squash; cook until wilted.
Drain noodles; transfer to bowl. Stir in cooked squash, remaining salt, pepper and 4 tablespoons Parmesan. Top with remaining Parmesan.
Remove toothpicks from chicken; slice on the diagonal into rounds.
. To serve, place 2/3 cup noodle mixture onto each plate. Fan slices out over noodles.