Cook rice according to package directions. Spread in greased 13x9-in. baking dish; set aside.
Meanwhile, preheat oven to 325°. Place asparagus and 1/2 in. of water in a large saucepan; bring to a boil. Reduce heat; cover and simmer 3-5 minutes or until crisp-tender. Drain and set aside.
In a large skillet, saute ham in 2 tablespoons butter until lightly browned. Spoon over wild rice.
In a large bowl, whisk eggs, milk, salt and pepper. In the same skillet, heat remaining butter until hot. Add egg mixture; cook and stir over medium heat until eggs are completely set. Spoon over ham; top with asparagus.
For sauce, heat oil in a saucepan. Stir in flour until smooth. Gradually stir in milk. Bring to a boil; cook and stir 2 minutes or until thickened. Reduce heat; add the cheese, ginger and pepper. Cook and stir 2 minutes longer or until cheese is melted.
Pour over casserole. Cover and bake 30 minutes. Uncover; bake 10-15 minutes longer or until a thermometer reads 160°.