Pat the fish fillets dry with paper towels. Trim away any thin edges and cut the fillets into 3/4-inch to 1-inch wide sticks (about 3–4 inches long). Season both sides lightly with 1/2 tsp kosher salt and 1/4 tsp black pepper.

Set up breading stations

Place the 1/2 cup flour in a shallow bowl or plate and spread evenly. In a second shallow bowl whisk the 2 large eggs with 2 tablespoons milk until combined. In a third shallow bowl combine 1 1/4 cups breadcrumbs, 1/4 cup grated Parmesan, 1/2 tsp garlic powder, 1/2 tsp paprika, 1/2 tsp kosher salt, 1/4 tsp black pepper and 1 tsp lemon zest (if using). Mix to distribute seasonings.

Bread the fish sticks

Working with a few pieces at a time, dredge each fish stick in flour, shaking off excess, then dip into the egg mixture, allowing excess to drip back into the bowl, then press into the breadcrumb mixture to coat thoroughly. Place breaded sticks on a baking sheet lined with parchment or a lightly oiled rack set over a sheet. Repeat until all sticks are breaded.

Preheat and prepare for baking

Preheat the oven to 425°F (220°C). If you have a wire rack, place it on a sheet pan and lightly spray or brush with oil; otherwise use parchment. Arrange the breaded fish sticks so they are not touching. Brush or lightly drizzle the tops with the 2 tablespoons olive oil or melted butter to promote browning.

Bake

Bake in the preheated oven for 10–14 minutes, turning once halfway through (about at 6–7 minutes), until the breading is golden and the internal fish temperature reaches 145°F (63°C) or the fish flakes easily with a fork. For extra crispness, broil on high for 1–2 minutes at the end—watch closely to avoid burning.

Dipping Sauce

While the fish bakes, whisk together 1/2 cup Greek yogurt (or mayonnaise), 1 tablespoon chopped fresh dill (or 1 tsp dried), 1 tablespoon lemon juice, 1 teaspoon Dijon mustard, 1/2 teaspoon honey, 1/4 teaspoon salt and 1/4 teaspoon black pepper in a small bowl until smooth. Taste and adjust seasoning or acidity with more lemon or salt as desired. Chill until ready to serve.

Finishing / Serving

Transfer baked fish sticks to a serving platter. Sprinkle with 1 tablespoon chopped parsley and serve immediately with the dill-yogurt sauce and lemon wedges on the side for squeezing. Leftovers keep in an airtight container in the refrigerator up to 2 days; re-crisp in a 400°F (200°C) oven for 6–8 minutes.