Preheat broiler to high.
Squeeze as much water from spinach as possible. Place in a medium bowl and add artichoke hearts, Monterey Jack, cream cheese, mayonnaise, shallot and garlic. Stir to combine.
Pat chicken dry and sprinkle with pepper and salt. Heat oil in a large cast-iron or other broiler-safe skillet over medium-high heat. Add the chicken to the pan and cook until browned, 2 to 3 minutes. Flip and cook for 1 minute more.
Top the chicken with the spinach mixture. Sprinkle evenly with Parmesan. Place the pan under the broiler and broil until an instant-read thermometer inserted in the thickest part of a cutlet registers 165°F and the topping is beginning to brown and warmed throughout, 2 to 3 minutes.
