Place a sheet of plastic wrap onto the counter. Place half of the prosciutto slices on top of the plastic wrap in a thin, overlapping layer. Spoon out half of the chilled duxelles onto the prosciutto layer and spread it out evenly. Place the chilled chicken onto the mushroom paste, along the edge closest to you.
Using the plastic wrap, carefully roll the chicken up in the prosciutto and duxelles. Once rolled up, twist the ends of the plastic wrap in opposite directions to tighten the roll, then tuck the ends under. Place on a plate and repeat with the second chicken breast. Place both chicken breasts into the refrigerator while preparing the puff pastry dough.
Roll out another sheet of plastic wrap onto the counter. Spray the plastic wrap with a little cooking spray, then add one sheet of puff pastry dough. Use a rolling pin to smooth out the dough. Remove the plastic wrap from the prosciutto-wrapped chicken and place on the puff pastry along the edge closest to you. Using the plastic wrap, roll the puff pastry around the chicken and cut off any overlapping dough with a sharp knife. Be sure to seal the sides of the chicken as well. Twist the ends of the plastic wrap in opposite directions and tuck the ends under, seam side down. Repeat with the other chicken breast, then chill the pastry-wrapped chicken breasts in the fridge for at least 20 minutes.
Preheat the oven to 425 degrees Fahrenheit. When ready to bake the chicken wellington, remove the chilled pastry-covered chicken breasts from the plastic wrap and place on a baking sheet seam-side-down. Brush with the egg yolk and sprinkle with salt. Bake in the preheated oven for 25 to 35 minutes, or until the puff pastry dough is golden brown and the chicken is warm throughout.
While the chicken Wellington is baking, prepare the mushroom sauce.