Halve each chicken breast and pound to 1/4 inch thick. Season, then place 4 salami slices, one cheese slice and 3 asparagus spears in center of each breast; roll up and secure with toothpick.
Spread 1/2 cup of sauce on bottom of an 11x7 baking dish. Put chicken in dish, top with remaining sauce and sprinkle with shredded cheese. Bake uncovered for 30-40 minutes, or until cooked through.