Preparation: Adjust oven rack to the lower-middle position and preheat to 350°F. Line three 8-inch cake pans with parchment paper and grease lightly with nonstick spray.
Mix Dry Ingredients: Sift together the flour and cocoa powder in a large bowl. Set aside.
Cream Butter and Sugar: In a stand mixer, beat butter, brown sugar, baking soda, salt, cinnamon, and vanilla extract on low speed until combined. Increase to medium and beat for 5 minutes, scraping the bowl halfway through.
Add Eggs: With the mixer running, add eggs one at a time, ensuring each is fully incorporated before adding the next.
Incorporate Dry and Wet Ingredients: Reduce the mixer speed to low. Gradually add one-third of the dry ingredients, followed by one-third of the red wine, alternating between the two until everything is fully incorporated.
Distribute Batter: Fold the batter gently with a spatula to ensure it’s evenly mixed. Divide the batter evenly between the prepared cake pans.
Bake: Bake for about 30 minutes, until the cakes are domed and firm. A toothpick inserted into the center should emerge with a few crumbs attached. Cool cakes completely in the pans, then invert onto a wire rack.
Assemble: Frost each layer with cream cheese frosting. Crumb-coat and frost the entire cake, then shave white chocolate over the top and sprinkle with cocoa nibs.