Preheat the oven to 375 degrees F. Heat the olive oil in a large, wide pot over medium heat. Add half of the garlic and half of the red pepper flakes and cook, stirring, until fragrant, about 1 minute. Add the spinach, in batches if necessary, and cook, tossing, until wilted. Transfer to a cutting board and chop. Transfer to a bowl and cool slightly. Add the panko, mozzarella, Parmesan, 1 teaspoon salt and pepper to taste and toss to combine.
Cut the stems off of the artichokes so that you have a flat base, reserving the stems. Cut the top 1 1/2 inches off the artichokes with a serrated knife and rub the surface with half of the lemon. Use kitchen shears to cut any remaining pointy tips from the artichoke leaves. Starting from the base, gently pull a leaf away from the center and stuff in a little bit of the spinach filling. Continue to stuff the leaves, working inward to the center of the artichoke, until it is no longer possible to pull the leaves away. Repeat with the remaining artichokes.
Arrange the artichokes in a baking dish and fill the dish with about 1 inch of warm water. Cover tightly with aluminum foil and bake until the leaves pull out easily and the flesh is tender, 1 hour to 1 hour 20 minutes. Let stand for 10 minutes.
Meanwhile, take the reserved artichoke stems and trim away all of the outer woody green parts, leaving just the pale green cores. Chop the cores. Melt the butter in a small saucepan over low heat. Add the remaining garlic, red pepper flakes and the stems. Cook, stirring occasionally, until the stems are crisp-tender and the butter is fragrant with garlic, about 6 minutes. Squeeze in the juice from the remaining lemon half and stir in the parsley; season with salt.
Serve the warm artichokes drizzled with the garlic-lemon butter; serve any remaining garlic-lemon butter on the side for dipping.