Stir together breadcrumbs, grated Parmigiano-Reggiano, ½ teaspoon kosher salt, black pepper, and garlic powder in a shallow dish.
Stir together flour and remaining 1/2 teaspoon kosher salt in a separate shallow dish.
Whisk together eggs and milk in a third shallow dish.
Cut zucchini into 3- to 4-inch x 1/2-inch sticks. Working in batches, dredge sticks in flour mixture, dip in egg mixture, and dredge in panko mixture, pressing to coat.
Arrange sticks in an even layer on a generously greased (with cooking spray) wire rack set on a baking sheet. Bake at 425°F until lightly browned and tender, about 25 minutes. Serve with warmed marinara sauce.