Preheat the oven to 335°F (168°C). Grease and line three 8-inch round cake pans.

Make the vanilla cake. In a large bowl, whisk together the sugar, milk, apple cider vinegar, yogurt, oil, and vanilla bean paste until smooth and emulsified.

Add the cake flour, cornstarch, baking powder, baking soda, and salt. Mix just until combined.

Divide the batter evenly between the prepared pans.

Bake for 22-25 minutes, until the tops spring back and a toothpick inserted into the center comes out with a few moist crumbs.

Cool the layers in the pans for 10-15 minutes, then turn them onto wire racks and cool completely. Once fully cool, wrap and refrigerate the layers until assembly.

Make the cookie dough lava. In a saucepan over medium heat, melt the butter with the brown sugar and granulated sugar until glossy.

Remove from the heat and whisk in the flour.

Stream in the heavy cream gradually until the mixture is molten but still thick.

Stir in the vanilla bean paste and salt. Let cool for about 5 minutes, then continue cooling until close to room temperature.

Fold in the mini chocolate chips. If the lava thickens more than you want, add milk a little at a time until it reaches your desired consistency.

Make the cookie dough. In a bowl, mix the butter, brown sugar, granulated sugar, flour, salt, vanilla bean paste, and enough heavy cream to make a soft dough. Fold in the mini chocolate chips.

Make the buttercream. Beat the butter for 2-3 minutes, until smooth and fluffy.

Add the powdered sugar, salt, and vanilla bean paste. Beat on low until combined, then whip on high until airy.

Stream in the heavy cream on low until the buttercream is smooth and silky.

Assemble the cake. Place the first chilled cake layer on a cake board or serving plate. Spread a thin layer of buttercream over the top, then pipe a tall buttercream dam around the edge.

Spoon cookie dough lava inside the dam and scatter pieces of cookie dough over the filling.

Repeat with the second cake layer, another thin layer of buttercream, a tall dam, cookie dough lava, and cookie dough pieces.

Top with the final cake layer and coat the cake with vanilla buttercream.

Finish the cake with more cookie dough lava and cookie dough pieces on top.

After the cake has been refrigerated, microwave individual slices for about 10 seconds to bring back the soft lava texture.