Pat walleye fillets completely dry with paper towels, pressing gently on both sides.

Season both sides of each fillet with kosher salt and black pepper, pressing the seasoning into the flesh.

Pour the all-purpose flour into a shallow dish and set up a dredging station.

Preheat a 12-inch skillet over medium-high heat for about 2 minutes, until a droplet of water sizzles on contact.

Add 1.5 tablespoons butter to the skillet and swirl until melted and foaming, about 30 seconds.

Dredge one fillet in flour, shake off excess, and place skin-side down in the skillet; cook undisturbed for 4 to 5 minutes until the skin is golden and crispy.

Flip the fillet with a fish spatula and cook the flesh side for 2 to 3 minutes more, until opaque and 145°F internal temperature; transfer to a plate and repeat with the second fillet, adding 1 tablespoon butter to the pan.

In a small saucepan over medium heat, melt the remaining 0.5 tablespoon butter with minced garlic, stirring for about 30 seconds until fragrant.

Squeeze lemon juice into the garlic butter, stir to combine, remove from heat, and stir in fresh parsley.

Place each fillet skin-side up on a warm plate, drizzle with lemon butter sauce, and serve immediately.