Preheat oven to 350°F. Lightly grease three 6-inch round cake pans and line with parchment paper. Set aside.
In a large bowl, whisk together flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, cream butter. Add vanilla paste and sugar and mix on medium speed until mixture is smooth. Scrape down bowl as needed to ensure thorough mixing.
Mixing on low speed, add eggs one at a time. Mix until eggs are incorporated.
Alternate adding flour mixture and milk in three addition, beginning and ending with the flour mixture. Mix until just combined. Add yogurt. Continue to mix on low speed until batter is throughly combined. Scrape down bowl as needed.
Divide batter among prepared cake pans. Spread batter into an even layer. Bake for 35-40 minutes until toothpick inserted in center of cake comes out clean. Allow to cool in pan for 5 minutes. If necessary, run a mini offset spatula around the perimeter of cake to loosen from pan. Unmold cake from pan and allow to cool to room temperature on wire rack.