Preheat oven to 375°F. Coat 16 cups of 2 muffin pans with the cooking spray. Cut the Monterey Jack into 16 small cubes.
Finely chop the artichokes and spinach and place in a medium bowl. Stir in the sour cream, garlic powder, and salt until well combined. Separate the biscuits and cut each in half to get 16 pieces.
Roll and stretch each piece of dough until very thin. Spoon 1 heaping tsp of spinach mixture onto center of dough. Place 1 cube of cheese on dip. Pinch dough tightly to close around filling. Place in 1 cup of muffin pan, seam-side down. Repeat with remaining biscuits and filling.
Lightly coat tops with cooking spray. Sprinkle tops with coarsely ground black pepper. Bake 15–20 min., until golden brown.