Heat oven to 425°F. Toss zucchini with 1 tablespoon oil and 1/4 teaspoon salt; roast on sheet 15 to 18 minutes until softened. Blot moisture; reduce oven to 375°F.
Meanwhile, cook noodles with tablespoon salt to 2 minutes short of package time; drain. Season chicken with remaining salt and pepper; skillet-cook in remaining oil 5 to 7 minutes to at least 165°F.
Melt butter in saucepan; whisk flour 1 minute. Gradually add milk and cream; simmer 4 minutes. Remove from heat; add Parmesan. Separately mix ricotta and egg.
Spread 3/4 cup sauce in 9-by-13-inch dish. Layer three noodles, half ricotta mixture, half chicken, half zucchini, one-third mozzarella, and 1 cup sauce. Repeat; finish with remaining noodles, sauce, and mozzarella.
Cover; bake 35 minutes, then uncovered 10 to 12 minutes until bubbling and center 165°F. Rest 15 minutes; cut eight portions.