Combine the glaze ingredients in a small pot over medium heat. Bring to a boil, then reduce heat to low. Simmer for about 10 minutes, crushing and stirring until the mixture is reduced to a soft puree. Strain the liquid into a small bowl, you will use it for glazing the cake. You can brush two or three coats over the cake. Set it aside until ready to use. The remaining solids can be used as jam.
Preheat oven to 375°F. Place a rack in the center of the oven. Grease a 9-inch springform pan and set it aside.
Using a stand or electric hand mixer, in a large bowl, beat the butter, sugar, vanilla extract, almond extract, lemon zest, and salt, until creamy.
After that, add the eggs one at a time and continue to mix, making sure to scrape the sides and bottom of the bowl a few times.
Next, little by little add the flour and the baking powder. Add the buttermilk and beat until the batter is just combined. Using a rubber spatula, fold in the shredded coconut.
Transfer the batter to the prepared pan and level the top with a spatula. Arrange the apricot halves, cut side down on top of the cake, pressing them VERY slightly - if you press too hard they will sink into the cake.
Bake for 35-40 minutes, or until a cake tester comes out of the center of the cake clean.
Remove the cake from the oven, place it on a wire rack, and let it cool for 10 minutes. After that, run a knife around the sides of the cake and loosen the springform wall. Sprinkle the top with sliced almonds.
Brush the top of the cake with the apricot glaze. Sprinkle with slivered almonds on top. Allow the cake to cool and serve with apricot jam on the side.
