Mise en place - Chop the chicken into bite-sized pieces. Destem and slice the mushrooms.
Cook the mushrooms - Add the mushrooms and a bit of salt to a dry pan over medium heat. Cook gently, stirring occasionally, until the mushrooms have expelled all of their water, then continue until the water has cooked off. Set the mushrooms aside and remove the pan from the heat.
Prep and cook the chicken - Put the pasta water on to boil. Generously salt the chicken and spray it with cooking spray. Separate the egg whites from the egg yolks. Save the yolks for some other purpose. Whisk the egg whites with the cornstarch until there are no lumps, then pour over the chicken pieces, tossing to coat. Sauté the chicken in the same pan that you used for the mushrooms. Sauté in batches until crispy and cooked through. Stash in a warming oven until you're ready to assemble the dish.
Boil the pasta - Once the water has come to a rolling boil, season the pasta water and cook the capellini according to the package directions. Drain the pasta.
Assemble and plate - Toss the pasta with mushrooms and fill individual serving bowls. Top with the crispy chicken and a generous dollop of pesto.