Lamb and Eggplant Shepherds Pie

Name: Lamb and Eggplant Shepherd's Pie
Ingredients: 1 1 1/2-pound eggplant, unpeeled, cut into 3/4-to 1-inch cubes; Coarse kosher salt; 7 tablespoons (or more) extra-virgin olive oil, divided; 2 pounds well-trimmed boneless lamb shoulder, cut into 1-inch cubes; All purpose flour; 3 cups chopped onions; 1 cup dry white wine; 1 28-ounce can diced tomatoes in juice; 3 cups beef broth (preferably organic); 8 garlic cloves, chopped; 1 tablespoon dried oregano; 2 1/2 pounds russet potatoes, peeled, cut into 1-inch cubes; 2 tablespoons (1/4 stick) butter; 2 tablespoons extra-virgin olive oil; 2 garlic cloves, minced; 3/4 cup whole milk; 1 1/4 cups (packed) coarsely grated kasseri cheese* (5 to 6 ounces)