In a mixing bowl, cream together 16 tablespoons of softened unsalted butter and 1 1/4 cups of granulated sugar until light and fluffy, about 3-5 minutes. Add in the zested lemons, 1 room temperature egg, 3 tablespoons of lemon juice, and 1 teaspoon of vanilla extract, mixing until smooth.

In a separate bowl, whisk together 2 2/3 cups of all-purpose flour, 1 teaspoon of baking soda, 1 teaspoon of baking powder, and 1/4 teaspoon of salt.

Gradually incorporate the dry ingredients into the wet mixture. Mix until a soft dough forms, being careful not to overmix.

Preheat the oven to 350°F (175°C). Scoop tablespoon-size portions of the dough onto a baking sheet lined with parchment paper. Bake for 10 minutes or until edges are golden. Let cool.

In another bowl, beat 8 ounces of softened cream cheese and 8 tablespoons of softened unsalted butter until smooth. Stir in lemon zest, remaining lemon juice, and powdered sugar until combined. Adjust consistency with heavy cream if necessary.

Spread or pipe frosting onto the flat side of one cooled cookie, then top with another cookie to form a sandwich. Repeat with remaining cookies.