In a medium bowl, sift together the flour, baking powder and 1/4 tsp. salt.
Using an electric mixer, cream 11 tbsp. butter and the granulated sugar on medium-low speed until fluffy, 3 minutes. Beat in the eggs and the extracts, scraping the bowl, for 2 minutes. Mix in the flour mixture in 2 batches on low speed.
Divide the dough between 2 pieces of plastic wrap. Using the wrap to help, shape the dough into 2 disks and seal. Chill for 2 hours.
Meanwhile, using the mixer, beat the remaining 10 tbsp. butter, 1/2 tsp. salt, the confectioners sugar, half-and-half, lemon juice and lemon zest on low speed until smooth. Beat on high speed until fluffy, about 2 minutes. Chill the filling.
Position racks in the upper and lower thirds of the oven; preheat to 375 degrees . Line 4 cookie sheets with parchment. Working with 1 dough disk at a time, roll out on a floured surface to 1/8 inch, rotating the dough as needed. Using a 2 1/2-inch cutter, cut out cookies. Divide the cookies among the pans, chilling the pans as you work.
Sprinkle the cookies with the sparkling sugar. Bake 2 pans at a time, switching them halfway through cooking, until the edges brown, about 8 minutes. Transfer the cookies to a rack; let cool.
Spread the bottom of 1 cookie with 1 tsp. of the filling. Sandwich with another cookie. Use your fingers to scoop and press the coconut onto the filling. Chill for about 30 minutes.