Preheat oven to 350°F. Beat sugar and butter with an electric mixer on medium speed until light and fluffy, about 2 minutes. Add egg yolks, 1 at a time, beating just until blended and smooth; beat in vanilla. Whisk together flour, baking powder, and salt in a medium bowl. Combine half-and-half and rum in a small bowl. Add flour mixture to butter mixture alternately with rum mixture, beginning and ending with flour mixture, beating on low speed just until flour mixture is incorporated after each addition.
Using clean, dry beaters, beat egg whites in a separate clean bowl on high speed until stiff peaks form. Gently fold into batter. Divide batter evenly among 3 greased and floured 8-inch round cake pans. Bake in preheated oven until a wooden pick inserted in center comes out clean, 23 to 25 minutes. Transfer to wire racks, and cool in pans 20 minutes. Remove cakes from pans to wire racks, and cool completely, about 1 hour.
Place 1 cake layer on a serving plate, and spread 1 cup Key Lime Buttercream over top. Place a second cake layer on top, and spread with 1 cup Key Lime Buttercream. Top with remaining cake layer, and spread top and sides with remaining Key Lime Buttercream. Top with Sugared Key Limes and Cranberries; garnish with mint leaves, if desired.
