Preheat the oven to 350°F and line a baking sheet with parchment paper.
In a large bowl, beat the softened butter and brown sugar together with an electric mixer until light and creamy.
Add the egg and vanilla extract and mix until fully combined.
Add the flour, baking soda, and salt to the bowl and mix on low speed just until a soft dough forms. Do not overmix.
Place the shredded coconut into a small bowl.
Scoop tablespoon-sized portions of dough and roll them into smooth balls.
Roll each dough ball in the shredded coconut until fully coated on the outside.
Place the coated dough balls onto the prepared baking sheet, spacing them about 2 inches apart.
Bake for 10–12 minutes, or until the edges are lightly golden and the centers are set but still soft.
Remove the cookies from the oven and immediately press your thumb or the back of a teaspoon gently into the center of each cookie to create an indentation.
Allow the cookies to cool on the baking sheet for 5 minutes, then transfer them to a wire rack to cool completely.
Once cooled, spoon lemon curd into the center of each thumbprint, filling the indentation.