Preheat oven to 350°F (180°C). Line two cookie sheets with parchment paper.
Toast the 1 tablespoon shredded coconut for sprinkling: place it in a small dry skillet over medium heat and cook, stirring constantly, until golden brown, about 1–2 minutes. Transfer to a small plate to cool.
In a food processor, combine 1/2 cup shredded coconut, 1/2 cup granulated sugar, 1 tablespoon lemon juice, 2 1/2 cups all-purpose flour, and 1 teaspoon vanilla extract. Pulse a few times to mix.
Add 1 cup (2 sticks) cold unsalted butter, cut into 1-tablespoon pieces. Pulse the processor in short bursts until the mixture forms a cohesive dough that holds together when pinched. The dough may look a bit dry at first.
Turn the dough out onto a lightly floured surface and lightly knead just until the dough is smooth and holds together. If it is still crumbly, press the pieces together with your hands until cohesive; do not add other ingredients.
Shape the dough into a ball, then roll it out to about 1/4 inch thickness on a lightly floured surface. Use cookie cutters to cut out shapes, rerolling scraps as needed.
Place the cut cookies on the prepared parchment-lined baking sheets, spacing them about 1 inch apart.
Bake in the preheated oven for 13–15 minutes, until the edges are set and just beginning to turn a pale golden color. Remove from oven.
Transfer the cookies to a wire rack and let them cool completely.
Melt the semi-sweet chocolate listed in the ingredients according to your preferred method. Drizzle the cooled cookies with the melted chocolate and immediately sprinkle each with the toasted shredded coconut. Let the chocolate set before serving.