Preheat the oven to 35o degrees F. Line two baking sheet with parchment paper or a silicone baking mat. Set aside.
Combine flour, baking powder, and salt in a small bowl. Whisk and set aside.
In a small bowl, add granulated sugar and lemon zest. Rub the sugar and lemon zest together with your fingers, until fragrant.
Beat butter and sugar/lemon mixture together until light and fluffy. Beat in egg, vanilla, and fresh lemon juice. Mix until smooth.
Slowly beat in flour mixture on low speed until blended. Drop dough by tablespoon onto prepared baking sheets, spacing 2 inches apart. Gently flatten dough with the palm of your hand.
Bake for 12-14 minutes or until cookies are just set and slightly golden brown. Cool cookies on baking sheet for 2 minutes and transfer to cooking racks. Cool completely.
While the cookies are cooling, make the Toasted Coconut Frosting. In a standing mixer, mix together butter and sugar. Mix on low speed until well blended and then increase speed to medium and beat for another 3 minutes. Add coconut extract and coconut milk. Beat on medium speed for 1 minute or until frosting is smooth and creamy. You may need to add a little more sugar or coconut milk, depending on your desired consistency.
Frost the cooled cookies with the coconut frosting. Sprinkle toasted coconut on top of each frosted cookies.
Note-store cookies in an air-tight container on the counter for up to 2 days.