Grease two 9-inch round cake pans and line the bottom of each with parchment paper. Grease the parchment paper, then dust with flour, tapping out excess. Heat oven to 350 degrees F.

Finely grind the coconut in a food processor, then transfer to a small bowl. Add pecans to the food processor, along with 2 tablespoons sugar, and finely grind them. Add to ground coconut.

In a large bowl, sift together flour, baking powder and salt. Stir in coconut and pecans.

In the bowl of a mixer fitted with the paddle attachment, beat butter, cream of coconut and the remaining sugar on high speed until light and fluffy, about 4 minutes. Add eggs one at a time, mixing well after each addition and scraping down the bowl as necessary, then beat in coconut extract.

Add the flour mixture in 3 batches, alternating with the coconut milk, starting and ending with flour mixture.

Divide batter between the pans and smooth the top of each with a spatula. Bake for 35 minutes, until cakes are golden and a tester comes out clean. Let cakes cool in the pans on a wire rack for 30 minutes. Run a knife around the edge of each cake, invert onto rack, and remove the parchment. Let cool completely.

Meanwhile, make the filling: beat egg yolks in a small heatproof bowl and set aside.

In a saucepan, combine condensed milk, butter and cream of coconut and cook over medium-low heat, stirring constantly, until hot, about 4 minutes. Whisk ⅓ of the hot milk into the egg yolks.

Transfer egg mixture to the saucepan of milk and whisk constantly over medium-low heat until mixture has the consistency of pudding, about 4 minutes. Do not let the custard get too thick. Transfer to a bowl and stir in the shredded coconut. Let cool completely.

Make the simple syrup: In a saucepan, heat sugar and ½ cup water, stirring occasionally, just until sugar has dissolved. Remove from heat.

Assemble the layer cake in a pan: Cut each cake in half horizontally. Place one layer in the bottom of the springform pan lined with parchment paper, moisten the top with 4 to 5 tablespoons simple syrup and spread ½ cup of the coconut filling in a thin, even layer with an offset spatula.

Repeat to make 2 more layers of cake and filling, then place the last layer on top. Put back the outside rim (collar) and tightly cover with a plate or wrap in plastic. Refrigerate cake for at least 1 hour or overnight.

Make the icing: Whip the cream with the confectioners’ sugar and coconut extract until stiff peaks form. Spread on the top and sides of the cake and sprinkle with toasted coconut.