How to Make It
Preheat oven to 350°F. Grease two 9-inch round cake pans with butter and line the bottoms with 9-inch circles of parchment paper; set aside.
In a bowl, whisk together flour, baking powder, baking soda, and salt. In the bowl of a stand mixer, cream together butter, sugar, and lemon zest on medium-high until lightened in color, about 4 minutes.
Add eggs one at a time, beating on medium and waiting until each is incorporated before adding the next. Add lemon juice, vanilla, and 1/2 cup yogurt. Beat on low until combined. Divide batter evenly among prepared cake pans and bake until golden brown and a toothpick inserted comes out clean, 25 to 27 minutes. Allow to cool before inverting out of cake pans, about 30 minutes.
Combine remaining 1/2 cup yogurt, cream, and powdered sugar in the bowl of a stand mixer and whip until medium peaks form. Refrigerate until ready to assemble cake.
Use a long serrated knife to remove the domes from each cake layer, making two level layers. Place one layer on a serving plate. Spread 1/2 cup lemon curd evenly over layer. Add 3/4 cup of whipped yogurt cream and spread evenly on top of layer of curd. Add second cake layer. Spread remaining lemon curd across layer, leaving a 1/4-inch border around the top edge of the cake. Add remaining whipped yogurt cream and spread almost to the edge of the layer of curd, allowing some of the curd to show around the perimeter of the cake. Refrigerate until ready to serve.