In a small mixing bowl, combine ½ cups of butter (1 stick) with all-purpose flour using a fork to form a creamy paste. Then, set aside.

Rinse the boneless, skinless chicken breast pieces under cold water and pat dry with a paper towel.

Place breadcrumbs on a plate, and ½ of the melted butter is used to brush all sides of the chicken lightly.

Cover the chicken in the breadcrumbs, then use a pastry brush to spread the remaining melted butter over the crumbs to keep them moist.

Place a grill pan over medium heat and set the broiler to low. Grill the chicken for about 5 minutes on each side until it's fully cooked. Then, remove the chicken from heat and set them aside.

Preheat your oven to 350 F.

In a big skillet that can be used in the oven, heat the chicken broth in the medium-high until it starts boiling.

After it starts boiling, stir in the butter-flour mixture. Keep stirring and bring the pot back to a boil until the sauce thickens, but it should be pourable.

Mix the lemon juice and wine in the sauce using a whisk, then reduce the heat to low and let it simmer.

Add the mushrooms and prosciutto to the sauce and let them simmer for 5 to 10 minutes.

Put the chicken breasts in the pan with the sauce.

Put cheese on top of each chicken breast piece. Then, put the skillet in the oven and bake the chicken until its cheese melts. It takes about 4 minutes.

Transfer the chicken on serving plates. Pour the sauce with mushrooms and prosciutto over the chicken. Enjoy with a vegetable topping.