Preheat the oven to 375°F (190°C) and spray a baking dish with olive oil spray.
Place the chicken breasts in the prepared baking dish in a single layer and season both sides with salt and pepper.
Bake the chicken uncovered for 15 minutes.
While the chicken bakes, chop or roughly chop the drained artichoke hearts and combine them in a mixing bowl with the squeezed spinach, chopped shallots, minced garlic, Greek yogurt, mayonnaise, Parmesan, and mozzarella; stir until evenly mixed.
Remove the chicken from the oven and spoon the spinach–artichoke mixture evenly over each breast.
Return to the oven and bake 20–25 minutes more, until the topping is bubbly and the chicken reaches an internal temperature of 165°F (74°C).
Let the dish rest about 5 minutes before serving.