Step 1

Arrange a rack in the middle of the oven and turn on the broiler to high. Meanwhile, cook the chicken and vegetables.

Step 2

Pat the chicken with paper towels, then season both sides of the cutlets with the sage, 1/2 teaspoon of the salt, and pepper.

Step 3

Heat 2 tablespoons 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 without crowding the pan, working in batches if needed. Sear the chicken until the bottom is browned, 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 minutes more. Transfer the cooked cutlets to a plate, tent with aluminum foil, and repeat cooking any remaining pieces.

Step 4

Reduce the heat to medium and add the remaining 1 tablespoon of oil. Add the potatoes, season with the remaining 1/2 teaspoon salt, stir to coat with the oil, and arrange in a single layer. Cook until the bottoms just start to brown, 3 to 4 minutes. Flip with a spatula and continue cooking until lightly browned and tender, about 3 minutes more. Stir in the spinach and garlic and cook until just wilted, about 2 minutes.

Step 5

Remove the skillet from the heat. Place the chicken on top of the vegetables in a single layer. Top each cutlet with a slice of prosciutto, then sprinkle with the cheese. Broil until the cheese is melted and bubbling, about 1 minute.