Save time the day of the party by preparing the crab mixture one day ahead. Cut and store the sliced bread in an airtight container until ready to assemble, and then broil as the recipe instructs shortly before party time.
Turn on broiler to high with oven rack in top position. Combine artichoke hearts, crabmeat, parsley, yogurt, mozzarella, Parmesan, lemon zest and juice, garlic, and black pepper in a large bowl; stir well to combine.
Spread about 2 tablespoons crab mixture on each baguette slice. Place on a baking sheet lined with aluminum foil. Broil until cheese begins to melt, 3 to 4 minutes (be careful not to burn toasts).