Preheat oven to 400 degrees F. In a medium saucepan cook potatoes, covered, in a small amount of lightly salted boiling water for 5 to 7 minutes or just until tender. Drain; transfer potatoes to a bowl and set aside.
For sauce, in the same saucepan combine cream cheese, milk, 2 tablespoons of the Parmesan, and the pepper. Heat and whisk until smooth and cheese melts. Remove from heat; stir in tarragon.
Layer half of the potatoes, ham, asparagus, and sauce in a 1-1/2-quart baking dish. Repeat layers. Cover with foil. Bake for 20 minutes. Remove foil; sprinkle with remaining Parmesan cheese. Bake 10 to 12 minutes more or until heated through. Let stand for 5 minutes before serving.