Shred the zucchini and place it in a colander; sprinkle with 1/2 teaspoon salt, toss, and let sit for 10 minutes to draw out moisture, then transfer to a clean towel or cheesecloth and squeeze until mostly dry.

Preheat the oven to 425°F and position a rack in the center; in a medium bowl beat 1 large egg with 1 tablespoon mayonnaise, then add 1/4 cup grated Parmesan, 1/3 cup flour, 2 tablespoons parsley, 2 minced garlic cloves, 1/4 teaspoon black pepper, and 1/2 teaspoon onion powder and stir to combine.

Stir the squeezed zucchini into the bowl and mix until the mixture holds together when pinched; if too wet add up to 1 tablespoon more flour.

Shape the mixture into rounded tablespoons or small patties about 1 1/2 inches across; press each lightly into 3/4 cup seasoned panko to coat both sides and place on a wire rack set over a rimmed baking sheet, spacing evenly.

Brush or drizzle the patties with the remaining 1 tablespoon olive oil to help browning.

Bake at 425°F for 14–16 minutes until the bottoms are golden and the centers look set, then broil on high for 1–2 minutes on the upper rack watching closely for deep golden color; remove and rest 3–4 minutes before serving.

To freeze, arrange coated, unbaked patties on a tray and freeze until solid, then transfer to a freezer bag for up to 2 months; bake from frozen adding 4–6 minutes to the bake time and broil briefly to finish.