Bring 1 quart water to boil and add 1 tablespoon salt.
Wash and pat dry duck gizzards and set aside.
Drop carrots into boiling water and blanch 1 minute. Remove to small mixing bowl and, while still warm, add red wine vinegar, oregano, salt and poppy seeds. Allow to cool in brine.
Cut leeks into 1-inch long half moons. Heat 2 tablespoons virgin olive oil in a 10-inch saute pan until smoking. Add leeks and saute until softened over medium heat, about 5 to 6 minutes. Add sugar and sherry and simmer until liquid is gone, about 4 to 5 minutes. Remove from heat and let stand.
Core and seed the pears and cut into 1/4-inch cubes. In mixing bowl, stir together Dijon, sherry, vinegar and extra virgin until smooth and add pears. In a 12-inch saute pan, heat remaining 3 tablespoons virgin olive oil until smoking. Season gizzards with salt and pepper. Place gizzards in pan, stirring constantly until cooked through, about 7 to 8 minutes.
To assemble dish, dress Mizuna with pear mixture and place in center of 4 plates. Sprinkle carrots around and arrange 3 piles of leeks on each. Divide gizzards over salad and serve.