To make the apricot jam, pit and slice apricots. Put them in a sauce pot with lemon juice,zest, and sugar. Cook down until thick, stirring frequently, until most of the water has evaporated. The fruit will break down but will still be chunky. This will take about 25 minutes. Chill apricot jam until ready to use.
To make olive oil cake, preheat oven to 350 degrees Fahrenheit. Combine olive oil and sugar in a mixing bowl fitted with a paddle attachment. Add in eggs, then alternate dry and wet ingredients. Line 2 8” pans with parchment paper and spray the sides with non-stick baking spray. Divide the batter between both pans and bake for about 35 minutes, or until edges pull away from the sides and a toothpick inserted comes out clean. Let the cakes cool at room temperature for 10 minutes, then invert into plastic wrap. Wrap and chill for 4+ hours, or overnight.
To make frosting, combine cream cheese and butter in a stand mixer fitted with a paddle attachment. Mix until smooth, add in powdered sugar,and mix until light and fluffy. Scrape down sides as needed. Transfer ¾ of the frosting to a piping bag.
To assemble, cut each cake in half. Use an offset spatula to smooth on a layer of cream cheese on the top of each cake. Make a dam by piping an edge of frosting on the edges of each cake. Fill center with apricot jam. Stack each cake on top of each other, filling the center of each with jam.Cover the sides and top with more cream cheese frosting and use an offset spatula to smooth out the cake.
Chill cake for 2+ hours before slicing and serving. Enjoy!