Prepare the Garlic Mashed Potatoes: Place cubed potatoes in a large pot, cover with cold water, and add a pinch of salt. Bring to a boil over high heat, then reduce to medium and simmer for 15-20 minutes until fork-tender. Drain, return to pot, and mash with minced garlic, warmed milk, butter, and salt until creamy. Cover to keep warm.
Pound and Season the Chicken: Place chicken breasts between plastic wrap and gently pound to ½-inch thickness using a meat mallet or rolling pin. Season both sides with salt and pepper.
Sear the Chicken: Heat 1 Tbsp olive oil in a large skillet over medium-high heat. Add chicken and cook 4-5 minutes per side until golden brown but not fully cooked. Remove and set aside.
Sauté the Vegetables: In the same skillet, add remaining 1 Tbsp olive oil. Sauté sliced mushrooms and hot peppers for 3-4 minutes until softened. Add 2 minced garlic cloves and chopped greens; stir until greens wilt, about 2-3 minutes. Stir in chopped prosciutto for 1 minute to crisp slightly. Remove veggies to a plate.
Make the Marsala Sauce: Reduce heat to medium. Melt butter in the skillet, whisk in flour to form a roux, and cook 1 minute. Slowly pour in Marsala wine, scraping up browned bits, and simmer 2 minutes to reduce. Add chicken broth, remaining 2 minced garlic cloves, salt, and pepper. Simmer 3-4 minutes until thickened.
Assemble and Finish: Return chicken to the skillet, spoon sauce over top. Place a slice of prosciutto and provolone on each breast. Cover and cook 5 minutes until cheese melts and chicken reaches 165°F internally.
Plate and Serve: On each plate, layer sautéed greens, top with chicken and sauce, and serve with a scoop of garlic mashed potatoes. Garnish with fresh parsley if desired.