This dish is served at the Parisian-style bistro Pastis in New York City and comes to us courtesy of co-chef Lee Hanson. It is garnished in simple French style with potatoes cut into seven-sided football shapes.
Bring a small pot of salted water to a boil. Slice off a little from each end of the potato. Cut potato in sixths lengthwise. Cut the wedges into elongated seven-sided ovals; hold potato wedge steady with fingertips and, with a small paring knife, trim all sharp edges. Work from top to bottom of piece in a quick curving movement, turning the piece slightly between each cut. The finished pieces should be of uniform size and shape. Add potatoes to boiling water. Reduce heat to low, and simmer until tender, about 15 minutes. Drain and reserve.
Bring stock to a boil in a medium saute pan. Reduce to a simmer. Season both sides of skate with salt and pepper. Place in pan; cover and cook 2 minutes. Turn fish. Cover once again, and cook until opaque, about 2 minutes more. With a fish spatula, transfer skate to two plates. Place three pieces of potato on each plate.
While fish is cooking, melt butter in a separate medium saute pan over high heat. Cook until butter starts to turn golden, about 1 minute. Remove from heat, swirling pan. This swirling motion combined with the remaining heat in the pan will bring the butter to its desired, almost-black color. Add lemon juice, capers, parsley, and a pinch salt and pepper. Spoon sauce over skate. Serve.