1. Preheat oven to 350 degrees. Butter two 9-inch round cake pans. Line bottoms with parchment. Butter parchment, and dust with flour; tap out excess, and set aside.

2. In a food processor, finely grind coconut; transfer to a bowl. Finely grind pecans with 2 tablespoons sugar, and set aside. Into a large bowl, sift together flour, baking powder, and salt; stir in ground coconut and pecans. Set aside.

3. In the bowl of an electric mixer fitted with the paddle attachment, beat butter, creamed coconut, and remaining sugar on medium-high speed until light and fluffy, about 4 minutes. Beat in eggs and extract. Beat in flour mixture in three batches, alternating with the coconut milk, and starting and ending with flour.

4. Divide batter between prepared pans; smooth tops. Bake until golden and a cake tester inserted in centers comes out clean, about 35 minutes. If tops begin to get too dark, cover loosely with foil. Let cool in pans 30 minutes. Run a knife around edges of cakes; invert onto a wire rack. Reinvert; let cool completely.

5. Line two rimmed baking sheets with plastic wrap; fit one with a cooling rack. Use a serrated knife to trim tops of cake layers, if desired. Transfer one layer to baking sheet with rack; spread with filling. Place remaining cake layer on top.

6. Using an offset spatula, spread 1 cup chilled ganache on sides of cake; smooth with a bench scraper. Pour remaining ganache over cake, coating completely. Transfer cake and rack to other baking sheet; chill until set, about 5 minutes. Scrape excess ganache back into bowl, passing through a sieve.

7. Coat the cake again with ganache. Chill until set, about 5 minutes. Press toasted coconut on sides of the cake, if desired. Keep at room temperature until ready to serve.