Preheat oven to 350 degrees F. Spray a sheet pan with nonstick cooking spray.
Use a serrated knife to cut slits roughly 1 1/2-inch apart across the bread front top to bottom and left to right, stopping before you slice all the way through the bottom (see photo above). Place bread in the center of the sheet pan.
Combine 3 Tbsp butter, 2 cloves of chopped garlic and parsley in a microwave-safe bowl. Heat until butter is completely melted, 1 to 2 minutes. Pour melted butter over the bread, moving the rows aside so that the butter gets down into the base of the bread.
Heat the remaining 3 Tbsp of butter in a saucepan over medium-high heat. When melted, stir in spinach and remaining 2 cloves of garlic. Saute until garlic is fragrant and excess liquid has cooked off the spinach, 3 to 5 minutes. Stir in artichokes and continue to cook until warmed through.
Remove the pan from heat and stir in mayonnaise, parmesan and mozzarella. Stuff filling into bread (this is easiest to do with your hands, but you can use a spoon if you're feeling classy).
Cover bread loosely with a piece of foil and bake for 30 minutes. Remove foil and continue to bake bread until the top is crisp and golden brown, 5 to 10 minutes more.