Preheat oven to 350°F. Grease and flour three 8-inch round cake pans.
In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large bowl, beat at medium high speed the sugars and butter until light and fluffy. Slowly add the oil and continue beating for 5-6 minutes until the mixture doubles in size. Scrape the sides of the bowl. Add eggs and egg yolks, one at a time, and beat until well incorporated. Scrape the sides of the bowl as needed.
In a 2-cup measuring cup, combine the yogurt, milk, and almond extract and mix until smooth.
Add one third of the flour mixture to the butter mixture, beat until just combined. Add half of the yogurt mixture and mix. Repeat the process ending with flour mixture. Scrape the sides of the bowl as needed.
Evenly divide the batter into the prepared pans. Bake for 25-30 minutes or until golden brown and a toothpick inserted in the middle of the cake comes out clean. Remove from oven and allow the cakes to cool in the pans for 10 minutes. Remove the cakes from pans and allow to cool completely.
Prepare the simple syrup by combining the sugar and water in a small saucepan. Bring the mixture to a boil, stirring occasionally. Remove from heat and add the almond liqueur. Allow the mixture to cool down.
Prepare the buttercream. In a large heatproof bowl, whisk together the eggs, sugar, almond extract, and salt. Place the bowl over a saucepan with simmering water. Whisk the mixture constantly and heat until it reaches 160°F. Remove from heat.
Beat the mixture at medium-high speed until light, fluffy, and cooled down to room temperature (this step is very important as if the mixture is too hot, the butter will melt). About 5-7 minutes. Reduce speed and slowly add the butter. The mixture may look curdle but it will smooth out as all the butter is incorporated. Once all the butter is added, beat at high speed for 1 minute until smooth and fluffy.
Assemble the cake. Place one cake layer on a serving platter. Drizzle with simple syrup. Using an offset spatula spread a layer of buttercream over the cake. Place another cake layer on top and repeat the process. Spread buttercream on top and sides of cake. Fill a pastry bag fitted with an oversized basket weave decorating tip with buttercream. Decorate the cake by piping buttercream in a diagonal motion. Top with chopped almonds and decorate the sides with slivered almonds.