Place walleye on a plate, skin side up, and chill, uncovered for one hour to dry out skin. Heat a large skillet over high, once the skillet is extremely hot add 1 Tbsp. oil and a large pinch of salt. Heat oil until smoking, then remove skillet from heat and wipe out with a clean kitchen towel to create a faux nonstick surface.
Season both sides of walleye with kosher salt. Return skillet to high heat and add remaining 1 Tbsp. oil until shimmering. Add 1 fillet skin side down. Press gently with a spatula until fillet no longer wants to curl up and entire skin side is flush with the skillet. Repeat with remaining fillet.
Cook both fillets in pan until nearly cooked through (fillet will be opaque and a bit raw at the thickest part), about 3 minutes. Gently turn fish and finish cooking off heat, about another minute or so.
