Season the chicken breasts with salt and pepper. Heat olive oil in a large skillet over medium-high heat, then add the chicken. Sear for 5-7 minutes on each side until golden brown and cooked through. Remove from skillet and set aside to cool.

In the same skillet, reduce heat to medium and add butter and a dash of olive oil. Sauté mushrooms, shallots, and garlic for about 8-10 minutes until moisture evaporates and mixture thickens. Allow to cool.

On a sheet of plastic wrap, lay out prosciutto slices overlapping slightly. Spread the mushroom duxelles over prosciutto, then place the chicken at the center. Roll prosciutto around chicken to create a tight log. Chill in refrigerator for 15-20 minutes.

Roll out puff pastry on a floured surface until large enough to wrap chicken roll. Place chilled chicken roll in the center and fold edges over tightly. Chill again for 10 minutes.

Preheat oven to 400°F (200°C). Whisk together egg yolk and water to create an egg wash. Brush the surface of the wrapped Chicken Wellington and cut small slits on top to allow steam to escape.

Transfer Chicken Wellington to a baking sheet lined with parchment paper. Bake for 25-30 minutes until pastry is golden brown. Let it rest for 5 minutes before slicing.