Preheat oven to 400 degrees F. In medium saucepan cook potatoes, covered, in small amount of lightly salted boiling water 5-7 minutes, just until tender. Drain; transfer to bowl and set aside.
For sauce, in same pan combine cream cheese, milk, 2 tablespoons of the Parmesan, and 1/4 teaspoon black pepper. Heat and whisk until smooth and cheese is melted. Remove from heat; stir in tarragon.
Layer potatoes, ham, asparagus, and sauce in 1 1/2-quart baking dish. Bake, covered, 20 minutes. Uncover; sprinkle with remaining Parmesan. Bake 10-12 minutes. Let stand 5 minutes. Top with tarragon and freshly ground black pepper.