Turn broiler on high.
Pat chicken dry with paper towels, then season both sides of the cutlets with the sage, salt, and pepper.
Heat 1 tablespoon of the oil in a 10-inch or larger cast iron skillet over medium-high heat, until shimmering. Add the cutlets in a single layer - do not overcrowd the pan.
Sear the chicken until the bottom is browned, about 3 to 4 minutes. Flip the cutlets and continue searing until the other side is browned and the chicken is cooked through, 3 to 4 more minutes. Transfer the cooked cutlets to a plate, loosely cover with aluminum foil, and continue cooking any remaining pieces.
Reduce heat to medium and add the remaining 1 tablespoon of oil.
Add the sliced potatoes, season with salt, and stir to coat the potatoes with the oil. Arrange in a single layer and cook until the bottoms just start to brown, about 5 minutes. Flip with a spatula and continue cooking until lightly browned and tender on both sides, about 4 more minutes. Stir in the mushrooms and garlic and cook until mushrooms shrink slightly and gain some color. Stir in the spinach and cook until just wilted, about 2 minutes.
Remove the skillet from heat. Place the chicken on top of the vegetables in a single layer. Top each cutlet with a slice of prosciutto, and sprinkle with the cheese. Broil until the cheese is melted and bubbling, about 1 minute.
Serve and enjoy!