In a medium-sized bowl whisk together the flour, baking powder, baking soda, and kosher salt. Whisk for 30 seconds to ensure the ingredients are well combined and that the baking powder and baking soda are well distributed throughout the flour.
Crack the eggs into a small bowl or measuring cup and beat them with a fork or small whisk
Place the unsalted butter, sugar, cardamom, vanilla extract, and almond extract in the bowl of a stand mixer. Start the mixer on low and mix for about 20 seconds, then increase the speed to medium and beat until the mixture is creamy and slightly lighter in color, about 2 minutes and 30 seconds. Scrape down the bottom and sides of the bowl and the paddle attachment.
Add the eggs one at a time, beating after each addition until the egg is fully incorporated into the creamed butter and sugar.
Add 1/2 of the flour mixture and mix on low until the flour is incoporated. There may be some flour on the sides of the bowl, which is okay. Add all of the sour cream and mix on medium until the sour cream is in incorporated. Add the remaining flour mixture and mix on low until incorporated. Scrape the sides and bottom of the bowl. Add the apricot puree and mix on medium until it’s incorporated and the batter has turned a light orange color.
Scrape the sides and bottom of the mixing bowl once more to ensure the batter is well mixed. For stand mixers ingredients often settle on the bottom and don't get completely mixed in with the other ingredients which is why it's imporant to scrape the bottom of the bowl and mix in any unmixed ingredients by hand.
Pour the batter into the prepared springform pan and use a silicon spatula to get all the batter out of the bowl. Smooth the top of the batter with an offset spatula.
Cut the apricots in half. Brush the insides lightly with a little bit of lemon juice. This step is to keep the insides from turning too brown as the cake bakes. Arrange the apricots, cut side up, around the edge of the pan and place one apricot half in the center. Depending on the size of the apricots you may need 3 or 4 whole apricots. Don't overcrowd the top of the cake. There needs to be enough room for the cake batter to rise and thoroughly bake.
Sprinkle the sliced almonds across the top of the cake batter. Make sure none of them are directly on the apricots.