Place sugar, red wine, tamarind candy, onion, ginger, and garlic in heavy large saucepan. Bring to boil over medium-high heat, stirring until sugar dissolves and tamarind candy melts. Boil mixture until syrupy, stirring frequently, about 8 minutes. Add chicken broth and 1 cup water; simmer over medium-low heat until thick and syrupy and reduced to 1 1/2 cups, stirring often, about 1 hour. Strain. (Tamarind sauce can be made 1 week ahead. Cover and refrigerate.)
Heat oil in heavy large skillet over high heat. Add duck and sauté until beginning to brown, about 3 minutes. Add leek, carrot, and mushrooms. Stir 1 minute. Add brown rice and stir until heated through, about 3 minutes. Add 1/4 cup tamarind sauce; stir to combine. Season to taste with salt and pepper. Stir in pea sprouts and serve.
*Precooked duck can be found in the meat or freezer section of many supermarkets.
