Preheat the oven to 350°F. Grease two 8-inch round cake pans and line the bottoms with parchment paper.
Place the 15 cookies for the cake in a zip-top bag and crush with a rolling pin into coarse, pea sized pieces. Crush the 12 cookies for the frosting into fine crumbs in a separate bag and set both aside.
In a medium bowl, whisk together the flour, baking powder, baking soda and salt. Set aside.
In a large bowl, whisk the buttermilk, yogurt and sugar until the sugar mostly dissolves. Whisk in the oil, melted butter and vanilla until smooth.
Add the dry ingredients to the wet mixture and fold gently just until combined. Fold in the coarse cookie pieces with just a few strokes, so the batter stays mostly white with dark speckles.Divide the batter evenly between the pans and smooth the tops.
Bake for 28-32 minutes, until a toothpick inserted in the center comes out clean. Cool in the pans for 10 minutes, then transfer to a wire rack and cool completely.
For the frosting, beat the butter on medium high for 3 minutes until pale. Add the powdered sugar, heavy cream, vanilla and salt, beat until light and fluffy, then fold in the fine cookie crumbs.
Place one cake layer on a plate, spread with frosting and top with the second layer. Frost the top and sides, then crush 2 of the topping cookies over the top.Press the remaining 8 cookies upright into the frosting around the top edge before serving.