Wash asparagus and break off tough bottom portion. Place two inches of water in a large skillet and bring to a boil. Carefully place asparagus in boiling water and cook for 1-2 minutes. Immediately remove from heat and rinse with cold water. Place asparagus on paper towels to dry.
In a large saucepan over low heat, melt butter. Whisk in flour and stir 4-5 minutes. Slowly add milk, stirring constantly. Simmer and stir until the sauce begins to thicken slightly; enough to coat the back of a spoon. Season to taste and remove from heat. Add 1/2 cup cheese (reserving remaining cheese for top of casserole) and stir until melted.
Assembly:
When ready to serve, preheat broiler. Roll each slice of ham around four asparagus spears and place in a lightly oiled 13 x 9 glass casserole dish, seam side down. Pour the cream sauce over the ham rolls and top with remaining grated Parmesan or Asiago cheese. Broil just until the ham rolls are heated through and the cheese is lightly browned. 4 servings.