Place yogurt in a fine sieve over a medium bowl. Cover and refrigerate. Let drain for 1 hour.

Preheat oven to 350°. Fit a steamer basket in a large pot with 1–2 inches water and add spinach. Bring to a boil and steam spinach until lightly wilted. Transfer to a colander and let cool. Wring out excess water.

Place spinach in a food processor. Add drained yogurt, 1/2 cup Parmesan cheese, mozzarella, mayonnaise, garlic, pepper, salt, and hot sauce. Process until coarsely blended. Add artichoke hearts and pulse until a chunky mixture forms.

Place mixture in a 1-quart baking dish and sprinkle with 2 tablespoons Parmesan cheese. Bake until bubbly and lightly browned, about 35 minutes.