Blanch and drain the asparagus. Cut into 1-inch pieces and set aside. Heat the oil in a large skillet and cook each tortilla until soft. Set on paper towels to drain. In a small saucepan, melt the butter. Add the flour, stirring to blend. Add the broth and cook until thick and bubbly, stirring constantly. Add the sour cream and taco sauce. Heat thoroughly.
Preheat the oven to 425 degrees F. Sprinkle each tortilla with 2 tablespoons cheese, chicken, onion, and asparagus. Top with 3 tablespoons of the cream sauce. Roll up and place, seam side down, in a baking dish. Sprinkle the remaining cheese over the top. Cover with the Parmesan and remaining cream sauce. Bake for 25 minutes.