Preheat oven to 350°F. Line cookie sheets with parchment paper or silicone mats.
In a large bowl, beat together cake mix, ricotta cheese, egg, and lemon zest for 2 minutes. Drop rounded teaspoons of cookie dough 2-inches apart on baking sheets. Bake for 10-12 minutes, or until set and bottoms are lightly golden.
Beat the cream cheese, butter, and 2 cups of powdered sugar. Add the ricotta and vanilla and mix until blended. Add additional powdered sugar to thicken, if necessary. Place in refrigerator to chill and set.
After frosting has set, spread or pipe onto the bottom of half the cookies. Top with remaining half of cookies. Refrigerate cookies until ready to serve.