Preheat the oven to 400°F (200°C) and spray a mini muffin tin with cooking spray.
Use a biscuit cutter or the rim of a glass to cut a 3-inch circle from each slice of sandwich bread.
Gently press each bread circle into a cup of the prepared mini muffin tin, crimping the edges with your fingers if desired.
Bake the bread cups for 3–4 minutes, until just lightly toasted.
Meanwhile, in a medium bowl combine the drained chopped spinach, chopped artichoke hearts, softened cream cheese, mayonnaise, sour cream, shredded mozzarella, grated Parmesan, and garlic salt; mix until smooth and evenly combined.
Spoon a heaping tablespoon of the spinach-artichoke mixture into each toasted bread cup and sprinkle extra Parmesan on top if desired.
Bake the filled cups for 5–6 minutes, until the filling is hot and the bread is golden brown.
Remove the cups from the muffin tin and serve warm.