Preheat oven to 400ºF (205°C). Carefully slice the chicken breast in half horizontally so that you end up with two thinner breast cutlets. Working one at a time, place a chicken breast cutlet between sheets of plastic wrap and flatten with a meat pounder or back of a frying pan into even thickness, about 1/4-inch, and season on both sides with salt and pepper.
Arrange the asparagus in a tight single layer on a baking sheet. Drizzle with 1 tablespoon of the olive oil. Season with salt and pepper. Turn the asparagus, so they’re evenly coated in the oil and seasonings and in a single layer. Roast until crisp tender, 12 to 20 minutes depending on the thickness of the asparagus. Reduce oven temperature to 300ºF (150°C).
Meanwhile, in a shallow bowl, stir together 1 tablespoon of the Dijon mustard, 1 tablespoon of the heavy cream, and 1 teaspoon water.
Place the chopped pecans in a shallow bowl.
Dip the chicken into the Dijon cream, then into the chopped pecans, turning and pressing gently to evenly coat each chicken piece with pecans.
In a nonstick sauté pan, heat the remaining 1 tablespoon olive oil over medium-high heat. Add the chicken and sauté for 3 minutes per side, 6 minutes total. Transfer the chicken to an 8-inch square pan, then bake for 12 minutes.
Meanwhile, deglaze the sauté pan with the remaining 3 tablespoons heavy cream, remaining 1 tablespoon Dijon mustard, and 1/8 teaspoon salt and a few grinds of pepper.
Serve the chicken with the Dijon cream sauce and roasted asparagus.