Preheat the oven to 350°F (175°C).
Lightly season both sides of the chicken breasts with salt and pepper.
If needed, pound the chicken to an even thin thickness or slice each breast in half lengthwise, then place the pieces in a 9x13 baking dish in a single layer.
In a medium bowl, stir together the chopped spinach, chopped artichoke hearts, grated Parmesan, mayonnaise, sour cream, and minced garlic until evenly combined.
Spread the spinach–artichoke mixture evenly over the top of each chicken piece, covering the surface completely.
Place a slice of mozzarella cheese on top of each stuffed chicken breast.
Bake in the preheated oven for 35–40 minutes, or until the chicken registers 165°F (74°C) and is no longer pink in the center.
Let the chicken rest a few minutes before serving.