Preheat oven to 400°. Lightly salt and pepper the chicken breasts. Spread 1 tsp mustard over the smooth side of each breast. Toss the potatoes (all liquid should be squeezed out) with salt and pepper. Firmly press about 1/2 cup grated potatoes on the top of each chicken breast. Heat the oil in a large nonstick skillet over medium-high heat. Cook the chicken, potato side up for three minutes. Carefully turn the chicken with a spatula and cook an additional 4-5 minutes, until potato topping is golden brown. Transfer the chicken, potato side up, to a lightly greased jelly roll pan and bake 10-12 minutes (or until chicken is cooked through).
Meanwhile, drain all but 1 TBS drippings from the skillet and saute the onion over medium heat for several minutes (until opaque). Raise the heat to medium-high and add the pepper and asparagus. Saute quickly, just until the vegetables are tender (1-2 minutes). Divide the vegetable mixture among four serving plates and top each with a chicken breast. 4 servings.
** Thanks to Jeanne Holan for trying a suggestion to grate the potatoes and hold in ice water until needed. She found that this will not work since the necessary starch is leached from the potatoes. To put together quickly, grate the potatoes using the proper disk in a food processor, and proceed with the recipe.