Heat the oven to 450°F Coat a rimmed baking sheet with olive oil cooking spray.
In a large skillet over medium heat, cook the panko, stirring frequently, until toasted, about 3 minutes. Transfer to a shallow bowl and stir in the Parmigiano-Reggiano and the oil.
In another shallow bowl, combine the flour with the garlic powder, then season it with salt and pepper. In a third shallow bowl place the egg mixture.
Working with several zucchini sticks at a time, toss them in the flour, shaking off the excess. Add the flour-coated zucchini to the egg mixture and toss to coat well, letting the excess egg drip off. Finally, place them in the panko mixture, tossing to make sure they are coated well on all sides. Arrange the fully coated zucchini sticks in a single layer on the prepared baking sheet.
Bake, turning once, until golden and tender, about 8 minutes.
While the zucchini is baking, in a small bowl stir together the mayonnaise, lemon juice, garlic and paprika. Season with and salt and pepper. Sprinkle the cooked zucchini lightly with salt and pepper, then transfer to a platter and serve immediately with the sauce.