Grease a 9-inch cake pan and line with greased baking parchment or wax paper. Preheat the oven to 350°. Drain the apricots and discard the liquid. Cut each half in half. Set aside.
Whisk together the flour, baking powder, baking soda and salt. Set aside.
In the large bowl of an electric mixer, cream together the butter and sugar for 3 to 4 minutes, or until the mixture is light in color and fluffy. Add the eggs, one at a time, beating until thoroughly mixed. Scrape down the bowl, add the vanilla and almond extracts, and mix until combined.
On low speed, add, in order, a third of the flour mixture, then half of the sour cream, then half the remaining flour mixture, the remaining sour cream and the remaining flour, mixing just to combine after each addition and scraping
down the sides of the bowl.
Pour the batter into the prepared pan and level it with a spatula. Arrange the apricot quarters in a decorative pattern on top of the batter. Sprinkle the sliced almonds over any exposed batter. Bake in the preheated oven for 45
to 50 minutes, or until a cake tester inserted near the middle comes out clean.
Let the cake cool in the pan for 10 minutes. Turn the cake out onto a plate, remove the parchment or wax paper liner from the bottom and then flip the cake onto a cooling rack.