Pound pork chops to 1/4 inch thickness. Melt 3 tablespoons of butter in a skillet over medium-high heat and brown pork on both sides, about 2 minutes per side. Drain fat. Pour water, vinegar, salt, and pepper in pan. Bring to a simmer, then reduce heat to medium-low, cover, and cook chops until tender, about 30 minutes. Remove chops from skillet, leaving juices, and place on a platter to keep warm.
Mash the anchovy fillets together with 2 teaspoons butter, and 1/2 teaspoon flour. Whisk this paste into the simmering liquid to thicken. Cook and stir until the liquid has thickened and the flour is no longer grainy, 3 to 4 minutes. Pour sauce over pork chops to serve.