Kosher salt, to taste
4 tablespoons unsalted butter, divided
2 teaspoons all-purpose flour, or as needed, for dusting
1/4 cup white wine
2 tablespoons finely chopped chives, garnish
Set the oven to warm or the lowest temperature. Have a baking sheet or oven-safe platter ready for the fish. Remove the skate wings from the refrigerator and salt lightly. Let stand for 15 minutes.
Heat a skillet over high heat for 3 minutes. Turn the heat down to medium-high and add 2 tablespoons of butter to the pan.
Meanwhile, dredge the skate wings in flour and shake off the excess.
Fry in the butter over medium heat, about 2 to 3 minutes per side.
Transfer the skate wings to the baking sheet and place in the warm oven.
Add the 2 remaining tablespoons of butter to the skillet. Cook over medium heat until the butter is light brown in color. Keep a close eye on the pan as this will not take too long, and you don't want the butter to burn.
Add the wine to the skillet (it will splatter, so be careful). Scrape up any bits that may have stuck to the bottom of the pan and cook off the alcohol, about 2 to 3 minutes.
Plate the fish and pour the sauce over the skate wings. Garnish with the chives and serve immediately.