Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a mixing bowl, cream together the butter and powdered sugar until light and fluffy.
Add lemon zest and vanilla extract, mix until well combined.
Gradually add the flour and shredded coconut, mixing until a dough forms.
In a separate bowl, beat the cream cheese and granulated sugar until smooth.
Scoop out tablespoon-sized balls of dough and flatten them into discs.
Place a dollop of the cream cheese mixture in the center of each disc.
Fold the dough over the filling, sealing the edges to form a cookie.
Bake in the preheated oven for 12-15 minutes, or until the edges are lightly golden.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.