Bring large pot of salted water to boil. Heat broiler, with rack set 4 inches from heat. In a medium bowl, whisk eggs. In another bowl, combine Parmesan and breadcrumbs. Season chicken with salt and pepper. Dip tenders in egg, then in Parmesan mixture; place on a rimmed baking sheet. Broil until golden, 2 to 4 minutes per side.
Preheat oven to 450 degrees. Spread 1 cup tomato sauce in the bottom of a 9-by-13-inch baking dish. Then top with chicken, remaining sauce, and finally mozzarella. Bake 15 to 20 minutes or until cheese is melted.
Meanwhile, cook pasta in boiling water until al dente, according to package instructions, adding broccoli for final 30 seconds. Reserve 1/2 cup pasta water; drain pasta and broccoli, and return to pot. Add oil and remaining Parmesan. Toss, gradually adding some reserved pasta water until pasta is lightly coated. Serve chicken with penne and broccoli.