Heat oven to 350°F. Combine the coconut, ¾ cup flour, ½ cup confectioners' sugar, 1 tablespoon cornstarch, and the butter in the bowl of a food processor. Pulse several times until a crumbly dough is formed. Press firmly into a greased 8-by-8-inch pan. Bake until just golden, about 12 minutes.
Sift together the granulated sugar, the remaining 1 tablespoon of cornstarch, and the 2 tablespoons of flour. In a separate bowl, beat the eggs, lime zest, lime juice, and vanilla. Slowly pour the egg mixture into the flour mixture, whisking to avoid lumps. Pour the filling over the baked crust.
Bake until the lime curd is set in the center, about 22 minutes. Cool completely in the refrigerator, about 2 hours. Cut into 16 bars and dust with powdered sugar before serving.