All ingredients ready? Let's begin!
In a small mixing bowl, combine 1 stick of butter with the flour using a fork to mix it all together into a creamy paste. Set this aside.
Rinse the chicken breasts under cold water and pat dry with paper towels.
Place the breadcrumbs on a plate. Lightly brush all sides of the chicken with ½ the melted butter.
Coat the chicken breasts in the breadcrumbs. Using a pastry brush, dab the remaining melted butter over the crumbs to moisten them.
Place a grill pan over medium heat, or turn the broiler on to the low setting. Grill or broil the chicken breasts for 5 minutes on each side until cooked through to an internal temperature of 165°F when checked with a digital meat thermometer. Set the cooked chicken aside.
Preheat or turn down your oven to 350°F.
In a large, oven-proof skillet over medium-high heat, bring the chicken stock to a boil.
Once boiling, whisk in the butter and flour mixture. Bring the pot back to a boil and continue to whisk until the sauce thickens but is still pourable.
Whisk the wine and lemon juice into the sauce and turn the heat down to a simmer.
Add the mushrooms and prosciutto to the sauce and allow to simmer for about 5 to 10 minutes.
Add the chicken breasts to the pan with the sauce.
Top each breast with cheese. Place the skillet in the oven and bake the chicken until the cheese melts, approximately 4 minutes.
Transfer the chicken to serving plates. Spoon the sauce with the mushrooms and prosciutto over the top of the chicken. Serve while warm with your favorite vegetables on the side.