Begin by preheating your oven to 350°F (180°C). Thoroughly grease the bottom and sides of a 9-inch springform pan with baking spray or butter and set aside.
In a food processor, blender, or with an immersion blender, blend half of the apricots with the lemon juice until smooth. Set this apricot purée aside.
Cut the remaining apricots into quarters and set aside for later use.
In a stand mixer fitted with a paddle attachment, cream together the softened butter and sugar on medium-high speed until the mixture becomes light and fluffy, approximately 4 to 5 minutes.
Add the eggs, one at a time, beating well after each addition. Then incorporate the vanilla extract and mix until well combined.
In a separate small bowl, whisk together the flour, baking powder, cinnamon, and salt. Gradually add these dry ingredients to the wet mixture, mixing until just combined.
Fold the apricot purée into the batter and mix until it is just incorporated.
Pour the batter into the prepared springform pan, spreading it evenly. Arrange the quartered apricots on top of the batter, distributing them evenly.
Bake in the preheated oven for 55 to 60 minutes, or until a skewer inserted into the center of the cake comes out clean, with just a few crumbs clinging to it.
Allow the cake to cool completely before dusting the top with powdered sugar for a delightful finish.