- Preheat oven to 350 degrees. Grease two 9-inch round cake pans and line bottom of each with a circle of parchment paper. Grease parchment paper then dust with flour, tapping out any excess.
- Make the cake: In a food processor, finely grind coconut then transfer to a bowl. Finely grind pecans and 2 tablespoons of sugar. In another large bowl, sift together flour, baking powder, and salt. Stir in ground coconut and pecans.
- In the bowl of an electric mixer fitted with paddle attachment, beat butter, cream of coconut, and remaining 1¾ cups plus 2 tablespoons sugar on high speed until light and fluffy, about 4 minutes. Beat in eggs one at a time, mixing well after each addition, then beat in coconut extract. Add flour mixture in three batches, alternating with coconut milk, starting and ending with flour mixture.
- Divide batter between prepared pans and smooth top of each with a spatula. Bake until cakes are golden and a tester comes out clean, 30 to 35 minutes. Let cakes cool in their pans on a rack for 30 minutes. Run a knife around edge of each cake then invert onto a wire rack; remove parchment. Let cool completely.
- While cakes are cooling, make the filling: Place egg yolks in a small heatproof bowl and set aside. In a small saucepan, combine condensed milk, butter, and cream of coconut and cook over medium-low heat, stirring constantly, until hot, about 4 minutes. Whisk a third of hot milk mixture into egg yolks to temper them. Transfer egg mixture to saucepan of milk and whisk constantly over medium-low heat until mixture has the consistency of pudding, about 4 minutes. Do not allow the custard to become too thick. Transfer custard to a bowl and stir in shredded coconut. Let cool completely.
- Make the simple syrup: In a small saucepan, heat sugar and water, stirring occasionally, until sugar has dissolved. Remove from heat.
- Assemble the cake: Cut each cake in half horizontally. Begin building the layer cake in a 9-inch cake pan: Place one layer in bottom of pan, moisten the top with a little simple syrup (you won’t need the full amount), and spread ½ cup coconut filling in a thin, even layer (use an offset spatula if you have one). Repeat with two more layers, then place final layer on top. Refrigerate cake for about 1 hour.
- Meanwhile, make the icing: In bowl of a stand mixer fitted with whisk attachment, whip cream and powdered sugar until stiff peaks form. Keep in refrigerator until ready to use.
- To unmold, run a spatula around edge of chilled cake, place a cake plate over top, and invert cake over onto plate. Spread whipped cream on top and sides of cake and sprinkle with toasted coconut. Refrigerate until ready to serve.