Fill a large mixing bowl with warm water and salt to create brine. Using a spoon, stir to combine until most of salt is absorbed before adding chicken breasts to bowl. Set aside to brine while prepping other ingredients, about 10 minutes.
Arrange oven rack on middle rack, preheat oven to 450 degrees F, and coat 9x13-inch baking pan with nonsticking cooking spray.
Remove chicken breasts from brine, rinse with cold water, then pat dry with paper towels.
In a small mixing bowl, mix all spices until well-combined.
In a large mixing bowl, combine chicken breasts, avocado oil, and about ¾ of spices, keeping some for seasoning the peppers. Using tongs, toss together until chicken is coated in spices.
Transfer chicken to prepared baking pan and spread cream cheese on top. Place peppers atop chicken. Sprinkle remaining spices on top. Sprinkle shredded mozzarella atop peppers.
Transfer pan to oven to bake until chicken is cooked to an internal temperature of 165 degrees F, about 15-17 minutes. Move oven rack to highest rack, turn on oven broiler, and broil until cheese is golden and bubbly, about 1-2 minutes, watching carefully to ensure it doesn't burn.
Remove pan from oven, top with optional garnishes, and serve.