Season the chicken cutlets evenly with the salt, black pepper, and garlic powder.
Heat the olive oil in a large skillet with a lid over medium heat.
Add the chicken cutlets and cook uncovered until golden brown on both sides, about 4 minutes per side. Remove the chicken and set aside.
In the same skillet, add the butter, asparagus, 1 tsp salt, and ½ tsp black pepper. Cook, stirring often, for 2 minutes.
Stir in the minced shallot, cover the skillet, and cook, stirring occasionally, until the asparagus is tender-crisp, about 3 minutes.
Pour in the heavy cream, raise the heat slightly, and let it simmer until the sauce thickens a bit, stirring often, about 3 minutes.
Return the chicken to the skillet, nestling it over the asparagus. Spoon some of the creamy sauce over the top.
Sprinkle with the chopped toasted walnuts and fresh parsley. Serve immediately.