For Buttercream Frosting
For Simple Syrup and Assembly
For cake, preheat oven to 325 °F and grease and flour 3 9-inch round cake pans.
Beat butter in a mixer fitted with the paddle attachment or with electric beaters until light and fluffy. Add sugar and again beat until fluffy. Beat in vanilla and add eggs, one at a time, blending well after each addition. In a separate bowl, sift flour, baking powder, baking soda and salt. Add flour, ½ cup at a time, mixing on a lower speed and alternating with buttermilk until all has been added and batter is smooth. Scrape batter evenly between the 3 prepared pans (I use a measuring cup to dole out the batter equally) and level with a spatula. Give the cake pans a gentle tap on the counter to loosen up any trapped air bubbles. Bake on center rack of the oven for 30 to 40 minutes, rotating pans halfway through cooking, until a center inserted in the center of the cake comes out clean. Cool cakes for 20 minutes, then turn out on a rack to cool completely.
For buttercream frosting, beat soften butter until fluffy and set aside. In a separate bowl whip egg whites with cream of tartar until foamy. Gradually pour in 3 Tbsp sugar while whipping and whip to soft peaks (whites will bend when whisk is lifted). Set aside.
In a small saucepot, bring remaining 10 Tbsp sugar and water to a boil. Continue boiling until temperature reads 239 °F (softball stage) on a candy thermometer. Remove from heat and immediately and carefully pour sugar syrup into whipped egg whites by pouring slowly down the side of the bowl while beating whites (pouring down the side of the bowl will prevent splashing). Beat whites on high speed until whites have cooled to room temperature. Once cooled, add soft butter, a little at a time until all has been added. Continue beating until buttercream is smooth and fluffy, about 2 minutes. Beat in vanilla and salt. Buttercream frosting can be used immediately. If using later, refrigerate, then soften to room temperature and beat with an electric mixer until smooth again.
For simple syrup, bring sugar and water to a simmer and cook until sugar is dissolved. Stir in vanilla and cool.
To assemble, place bottom layer on a plate and brush lightly with simple syrup (this keeps cake moist and makes spreading frosting easier). Dollop buttercream on top and spread smoothly, to about ¼ -inch thick, pushing frosting right to the edges. Spread redcurrant jam over buttercream. Place second cake layer on top and repeat brushing with syrup, jam and frosting. Place final cake layer on top. Chill cake until ready to present and serve, but let sit at room temperature for 15 minutes before slicing. Dust top of cake generously with icing sugar