Make cake layers:
Turn oven to 350°F and bake pecans in upper third of oven and coconut in lower third, stirring occasionally until golden, by then oven should be preheated.
Oil cake pans. Line bottoms of pans with rounds of parchment or wax paper.
Sift together sugar, flour, cocoa powder, baking powder, baking soda, and salt into a large bowl.
Whisk together whole milk, butter, whole egg, yolk, vanilla, and almond extract in another large bowl until just combined.
Beat egg mixture into flour mixture with an electric mixer on low speed, then beat on high speed 1 minute. Reduce speed to low and beat in water until just combined (batter will be thin).
Divide batter among cake pans. knock pans to remove some air bubbles and bake in upper and lower thirds of oven, switching position of pans and rotating them 180 degrees halfway through baking, until a tester comes out clean, 20 to 25 minutes total.
Cool layers in pans on racks 15 minutes. Run a thin knife around edges of pans and invert layers onto racks. Carefully remove parchment or wax paper and cool layers completely.
Heat a tall pot of water, enough to cover the can of unopened condensed milk and let it cook for 1 1/2 hours on low heat. When done, remove from water and allow to cool before opening . Open can and pour into a bowl, stir in coconut, pecans, and vanilla , covered with foil.
Make glaze while milk is baking:
Melt butter in a 3-quart saucepan. Remove pan from heat and add chocolate and corn syrup, whisking until chocolate is melted. Transfer 1 cup glaze to a bowl, reserving remaining glaze at room temperature in pan. Chill glaze in bowl, stirring occasionally, until thickened and spreadable, about 1 hour.
Before assembling, trim and level cakes. Put 1 cake layer on a cardboard base and then on a rack set over a baking pan (to catch excess glaze).
Use your fingers to drop half of coconut filling evenly over layer and make sure that it is spread right to the edge of cake. Top with another cake layer and spread with remaining filling in same manner. Top with remaining cake layer.
Spread chilled glaze evenly over top and side of cake.
Heat reserved glaze in pan over low heat, stirring, until glossy and pourable, about 1 minute. Pour glaze evenly over top of cake, making sure it coats sides. Shake rack gently to smooth glaze. Chill cake until firm, about 1 hour.
Transfer cake to a plate.
Cake keeps, covered and chilled, 3 days.
Bring to room temperature before serving.