Lemon Poppyseed Layer Cake With Whipped Yogurt Buttercream

Preheat the oven to 350 degrees F. Line a 9" x 13" pan with parchment paper and grease the paper.
Cream together the butter and sugar until light and fluffy. Add the vanilla and eggs, one at a time, and beat to combine well.
Add the rest of the cake ingredients, mix until just combined, and pour the batter into your prepared pan.
Bake for 20-30 minutes--the cake is ready when it just springs back to the touch and starts to pull away from the sides of the pan. Let cool completely in the pan.
While cake cools, make the frosting. Beat the butter in a stand mixer until very fluffy (at least 4 minutes). Add the confectioners' sugar slowly and beat to combine.
Add the yogurt in three additions, beating well between each to keep the frosting fully. Add the vanilla bean paste and lemon zest and beat well. If your frosting gets too soft, chill it for 10 minutes in the refrigerator before continuing.
To assemble, slice the cooled cake into four rectangles. Place one on a plate, top with 1/4 cup of lemon curd, then another layer of cake. Top with a thin layer of the frosting and then 1/4 cup of the lemon curd, then another layer of cake. Repeat, only using the lemon curd (although you can add frosting in each layer too! I prefer to use less buttercream) until you put the top layer on, the frosting the top and sides with the remaining buttercream.