Remove roots and tough upper leaves from leeks. Cut each leek in half lengthwise. Cut each half crosswise into 1/2-inch-thick slices (you should have about 6 cups). Soak in cold water to loosen dirt.
Combine leeks, 1/2 cup water, 1 teaspoon butter, 1/4 teaspoon salt, and 1/4 teaspoon pepper in a large Dutch oven or deep sauté pan over medium-high heat. Cook for 10 minutes or until leek wilts. Pour the leek mixture into a bowl.
Heat remaining 2 teaspoons butter in pan over medium-high heat. Add pork to pan. Cook 5 minutes, turning to brown on all sides. Add remaining 1/4 teaspoon salt, remaining 1/4 teaspoon pepper, and wine to pan; cook 15 seconds, scraping pan to loosen browned bits. Return leek mixture to pan. Cover, reduce heat, and simmer 2 hours or until pork is tender. Remove pork from pan. Increase heat to reduce leek sauce if too watery. Cut pork into 1/4-inch-thick slices. Serve with leek mixture. Garnish with parsley, if desired.