Preheat oven to 350°F (180°C). Spray an 18x13-inch rimmed baking sheet with cooking spray; line pan with parchment paper, and spray pan again.

In a small saucepan, melt butter over medium heat. Remove from heat, and stir in molasses, grated ginger, and vanilla. Set aside.

In the bowl of a stand mixer, whisk together eggs, brown sugar, and egg yolk by hand. Place bowl over a saucepan of simmering water. Cook, whisking occasionally, until an instant-read thermometer registers 110°F (43°C), about 5 minutes. Return bowl to stand mixer fitted with the whisk attachment, and beat at high speed until thick and tripled in volume, about 5 minutes.

In a medium bowl, place about 1 cup egg mixture. Fold in warm butter mixture. Set aside.

In a small bowl, sift together flour, cornstarch, ground ginger, cinnamon, salt, nutmeg, and cloves. Using a large balloon whisk, gently fold flour mixture into remaining egg mixture in two additions just until combined. Fold in butter mixture. Using an offset spatula, quickly and gently spread batter evenly in prepared pan.

Bake until cake starts to pull away from sides of pan, 12 to 15 minutes. Let cool completely in pan.

Loosen cake from sides of pan, if needed. Using a serrated knife, cut into 4 (12x4-inch) rectangles. (You will have some cake edges left over.) (Be sure to cut through the parchment paper as well; use scissors if needed). Lift each piece, with parchment attached, out of pan. Brush with Molasses Simple Syrup. Spread ⅔ cup Brown Sugar Buttercream on each rectangle.

Roll up 1 rectangle, jelly roll style, and place in center of a cake plate. Remove parchment. Carefully wrap a second rectangle around center roll, using parchment to help. Remove parchment, and repeat with remaining rectangles, creating a spiral. Using a serrated knife, trim end of final piece at an angle to make it flush with outer edge of cake.

Spread remaining Brown Sugar Buttercream on outside of cake. Without adding additional buttercream, lightly spread buttercream that peeks through the layers on top. Place White Chocolate Bark vertically on sides of cake, overlapping slightly and pressing into buttercream to hold in place. Cover and refrigerate for at least 2 hours or overnight. Let stand at room temperature for 1 hour before serving.