Preheat your oven to 350°F (177°C). Grease three 8-inch cake pans and line the bottoms with parchment paper rounds. Dust the sides with a little flour and tap out the excess.
In a medium bowl, whisk together 3 cups all-purpose flour, 2½ tsp baking powder, 2 tsp cinnamon, and 1 tsp fine salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat 1 cup (2 sticks) room temperature butter, 1 cup granulated sugar, and 2 cups packed brown sugar on medium-high speed for 3–4 minutes until light and fluffy. Scrape the bowl once or twice.
Turn the mixer to low. Add 2 Tbsp oil, 2 tsp vanilla, and 1 cup room temperature egg whites in a slow, steady stream. Mix until just combined.
Add the flour mixture in three additions, alternating with 1½ cups buttermilk, starting and ending with flour. Mix on low until a few streaks of flour remain, then fold by hand with a rubber spatula until just combined.
Divide the batter evenly among the three pans (about 640g per pan). Bake for 22–27 minutes until the cakes spring back lightly and a toothpick inserted in the center comes out clean or with a few moist crumbs. Let cool in pans for 10 minutes, then turn out onto a wire rack to cool completely.
Make the vanilla buttercream: In a clean mixer bowl with the paddle attachment, beat 3 cups (6 sticks) room temperature butter on medium speed for 2 minutes until smooth. Add 1 Tbsp vanilla and 1½ tsp salt. Gradually add 10 cups powdered sugar, one cup at a time, on low speed. Add ½ cup heavy cream and mix until incorporated, then whip on medium-high for 3–4 minutes until light and fluffy.
Reserve about 1½ cups of the vanilla buttercream for another use (or eat it). To the remaining buttercream, add 1 cup cookie butter and mix until combined. In a small saucepan, warm the other 1 cup cookie butter with ¼ cup heavy cream over low heat, stirring until smooth and pourable — this is your soak and drip.
Place one cooled cake layer on a serving plate. Use a pastry brush to generously soak it with the warm cookie butter mixture. Spread about ½ cup of cookie butter frosting over it. Repeat with the second and third layers. Apply a thin crumb coat to the entire cake and refrigerate for 20–30 minutes until set.
Apply the final generous layer of cookie butter frosting. Top with crushed Biscoff cookie pieces and drizzle with the remaining cookie butter soak. Let the cake sit at room temperature for 30 minutes before slicing.