4. Bring a large pot of water to a boil over high heat. In the meantime, place a large sauté pan over medium-high heat and add the vegetable oil. When the oil is hot, use a spatula to carefully transfer the walleye fillets to the pan. Cook for about 3 minutes, or until golden brown on the bottom, then flip and cook for another 3 to 4 minutes, or until done.