Butter and lightly flour the insides of a 10-inch round cake pan.
Sift together the flour, polenta, baking powder and salt. Set aside.
In a mixer, on medium speed, cream the butter until light and fluffy. Add 1 cup of the sugar and beat until pale and fluffy Add almond paste and beat again. Blend in vanilla and almond extracts, then beat in the egg yolks, 1 at a time, being sure that each is mixed in before the next is added. Alternately, beat in small amounts of the sifted dry ingredients and the cream to the butter mixture, beginning and ending with dry ingredients.
In a clean mixer, beat egg whites until opaque, then add remaining 1/4 cup sugar and beat until whites form soft peaks. Fold into batter gently but thoroughly. Pour the batter into the cake pan. Bake on the middle shelf of the oven for about 60 minutes, or until a tester inserted in the center comes out clean. (Do not test or move the cakes before they have baked for at least 45 minutes since they are delicate and may fall.)
Allow the cake to cool and when cooled remove from the pan and dust the top with powdered sugar. Cut into eighths or tenths.
Serve this cake with summer fruits —peaches, nectarines, apricots, berries¿—tossed with a little sugar, freshly squeezed lemon juice and a pinch of gray salt.