Cover the bottom of a 9-inch cake pan with a round of parchment paper. Oil the entire pan, then dust with flour and tap out excess.
Preheat oven to 375°F.
Melt the butter and chocolate together in a bowl set over a pot of gently simmering water, removing from heat when almost completely melted and stirring until smooth.
While the chocolate is melting, pour the pomegranate juice into a small saucepan and boil it down until it is reduced by about half.
To the melted chocolate, stir in the juice, almond extract, and salt, and set aside to cool.
In a small bowl, stir the flour and almond meal together, and set aside.
In a large bowl, whisk the egg yolks together with 1/2 cup sugar until well blended. Stir in the chocolate mixture.
Beat the egg whites and cream of tartar until they reach soft peaks. Gradually add the remaining 1/4 cup sugar and keep beating until they reach stiff peaks.
Fold the almond meal and flour and about 1/4 of the egg whites into the chocolate mixture. Once incorporated, fold in the rest of the egg whites.
Pour into prepared pan.
Bake for 25 minutes, or until a toothpick inserted about 1 1/2 inches from the edge comes out clean, but a toothpick inserted into the center still comes out slightly gooey.
Place the cake pan onto a rack and let it cool. It will deflate, but that is what is supposed to happen.
When cooled, invert onto a serving plate and remove parchment paper from top. Trim the top and edges if desired, then cover with chocolate ganache or a dusting of powdered sugar.