Preheat oven to 350F.Butter, and flour cake pans or a rimmed baking sheet. Line the bottom with parchment.
Combine flour, ground walnuts, baking powder, and salt in a bowl. Set aside.
At medium speed, beat egg whites with cream of tartar until soft peaks are formed. Gradually add about half of the powdered sugar, increase the speed to medium-high, and beat until stiff and glossy peaks are formed, don't overbeat, or the meringue will become grainy and dry.
In a mixing bowl, beat egg yolks with the remaining sugar, for about 5 minutes, until thick and pale in color. Gradually add warm water and vanilla extract.
Gradually, into the egg yolk mixture, gently fold in the dry mixture, and meringue, until you can't see any more white streaks.
Divide cake batter into prepared pans.
Bake for 25-30 minutes or until toothpick inserted into the cake comes out clean.
Let the cakes cool in the pan for 10 minutes, then carefully remove the cakes from the pan and onto a cooling rack.
FLOUR BUTTERCREAM
Add flour to 1 cup of milk, and whisk until smooth. Stir in the remaining milk. Pour the flour mixture into a pot.
Cook on medium-high heat, and bring the mixture to a slow boil, continuously stirring; it will start to thicken and look like a thick pudding. To cook off the flour taste continue cooking additional 2 minutes, stirring. Strain the flour pudding through a fine mesh sieve. Cover hot pudding with plastic wrap and let it cool to room temperature. Speed up the cooling with a cold water bath.
Beat room temperature butter, add powdered sugar, beat until smooth, and gradually add room temperature flour pudding.
Beat until fluffy and creamy. Beat in the vanilla bean paste or vanilla extract.
GANACHE DRIP
Heat heavy cream until it is hot and tiny bubbles form on the surface; pour it over small pieces of chocolate and let stand for 1 minute. Gently whisk until smooth. Don't move the whisk in multiple directions; this can lead to too many air bubbles.Let it cool to room temperature for about 10-15 minutes. Pour on a well-chilled cake.