1. Preheat oven to 325°. Butter two 9-in. cake pans; set aside.
2. Make cake: In a large bowl, sift together flour, baking powder, and salt. Set aside. In the bowl of a stand mixer, beat butter and sugar together on low speed until light and fluffy. Add egg whites in 3 batches, scraping inside of bowl as needed. Beat in flour mixture in 5 batches, adding 1/4 cup water after each addition (you will begin and end with flour); make sure flour is completely blended each time before adding water. Pour batter into prepared pans, dividing evenly. Smooth tops with a spatula.
3. Bake until center of cake feels firm to the touch and a toothpick inserted in center comes out clean, about 40 minutes. Cool cakes completely in pans on a rack.
4. Meanwhile, make cranberry filling: Combine 3 cups cranberries, the sugar, preserves, and 1/4 cup water in a small saucepan and cook over high heat until cranberries pop and preserves melt, 5 to 10 minutes. Add remaining 3/4 cup cranberries, stir to combine, and remove from heat. Transfer to a small bowl and chill until ready to assemble cake.
5. Make buttercream: Fill a 2-qt. pan with about 1 in. water and bring to a simmer over low heat. Put egg whites, salt, and sugar in the bowl of a stand mixer and whisk to combine. Place bowl over hot water, making sure bottom of bowl isn't touching water, and heat whites, whisking constantly, until hot to the touch, 3 to 5 minutes. Remove pan and bowl from heat.
6. Put bowl of warm whites on the mixer and whisk on high speed until tripled in volume and side of bowl is cool to the touch, about 10 minutes.
7. Meanwhile, chop 4 oz. white chocolate, put in a medium metal mixing bowl, and set in same pan of warm water off the heat to melt slowly, stirring occasionally. Remove bowl from pan and let cool to room temperature.
8. Reduce mixer speed to low and whisk butter into whites, about 1/4 cup at a time, until incorporated. Continue to whisk on low speed until smooth and fluffy, about 10 minutes (mixture may look grainy at some point but will come together).
9. With a rubber spatula, gently fold melted chocolate into buttercream until completely combined.
10. Assemble: Rub tops of both cakes gently with your hands to remove browned outer surface, then carefully invert cakes and rub undersides so that cakes are completely white. Place 1 cake layer on a cake stand or serving plate, top side up. Using a pastry brush, brush top with half the liqueur. Spread about 1 1/2 cups cranberry mixture over layer with a metal spatula, leaving a 1/2-in. empty border around edge. Place second cake layer on top, flattest side down, and brush with remaining liqueur. Spread top and sides of cake with a thin layer of buttercream to seal in crumbs and chill 30 minutes. Cover with remaining buttercream, starting with the sides and covering the top last.
11. Use the palm of your hand to warm remaining chocolate. Shave smooth side of chocolate bar with a vegetable peeler to make thin curls; scatter curls over cake's top. Sift powdered sugar over cake. Serve with remaining cranberry mixture on the side.
Make ahead: Baked cake layers can be wrapped in plastic and stored at room temperature or in the fridge up to 2 days ahead. Cranberry filling can be made up to 2 days ahead and chilled.
Bakers' tip: To make a pure white cake, use your fingers to rub off the browned surface of each layer before assembling.
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