Season the skate with salt and pepper on both sides and dredge in flour to lightly coat, shaking off any excess flour. In a large skillet, add vegetable oil and heat until hot but not smoking. Add 2 tablespoons of the butter and, when melted, saute skate for 3 minutes on each side, or until golden brown on both sides. Transfer to a warm plate and set aside while you make the sauce.
With a paper towel carefully wipe out skillet and return to heat. When skillet is hot add remaining 6 tablespoons of butter and allow to cook until butter just begins to brown and has a nutty fragrance. Add lemon juice, parsley, and capers, and stir to combine well. Taste, season with salt and pepper, and serve immediately over hot skate fillets.