Preheat the oven to 450ºF.

Put the potato sticks in a large bowl of water and cover with hot tap water.  Let sit for 10 minutes.

Drain the potatoes and spread them on a large kitchen towel.  Dry them well.  Set a wire rack inside a large baking sheet.  Place the potatoes in a large bowl with the oil and toss well.  Lay the potatoes out in a single layer on the wire rack.  Season with the salt.  Bake until they are golden brown and crispy, about 40 minutes.

20 minutes before the potatoes are finished, start the fish.  Combine the panko, garlic, parsley, lemon zest, salt and pepper in the bowl of a food processor.  Pulse until you have fine crumbs.  Pour the crumbs into a wide, shallow bowl. 

In a separate shallow bowl, lightly whisk the eggs. Dip the fish in the egg mixture, letting excess drip off, then dredge in the breadcrumb mixture.  Press the mixture into the fish to coat.  Transfer the fish to a plate and repeat with the remaining fish.

In a 12-inch nonstick skillet set over medium-high heat, melt 1/2 tablespoon of butter.  Add 2 pieces of the fish and cook until the bottom of the fish is browned and crispy, 3 to 4 minutes.  Flip and cook the fish on the second side for 3 minutes more, until browned.  Transfer to a warm plate. Melt the remaining 1/2 tablespoon of butter in the skillet and repeat with the remaining 2 pieces of fish.

Serve the fish with the potatoes.