Preheat oven to 350 degrees. Place artichokes in a large stockpot; cover with water by 3 inches. Halve 4 lemons; squeeze juice into water, and add rinds. Bring to a boil. Cover; cook 20 minutes. Transfer artichokes to a wire rack set over a rimmed baking sheet; let drain upside down. Let cool completely. Remove leaves, reserving 3 cups. For each artichoke, trim inner part to the heart; scrape out fuzzy choke, and discard, reserving heart.
Put spinach into a steamer basket set over boiling water. Cook until wilted, about 2 minutes. Let cool. Squeeze out water, and coarsely chop spinach.
Pulse artichoke hearts, the finely grated zest and juice of remaining lemon, the mayonnaise, shallot, garlic, ricotta, salt, and cayenne in a food processor until combined; season with pepper. Transfer to an ovenproof dish. Stir in spinach and 1/3 cup plus 1 tablespoon mozzarella. Sprinkle with Parmesan and the remaining tablespoon mozzarella.
Heat dip in oven 10 minutes. Remove from oven. Preheat broiler. Broil dip until edges are bubbling and top is golden brown, 2 to 3 minutes. Serve dip with artichoke leaves and toasted baguette.
On "Mad Hungry with Lucinda Scala Quinn," Lucinda used 6 artichokes instead of 5 to make the dip.