A drum-shaped nut grinder is the best tool for grinding pecans. You can also use a food processor; add one tablespoon of the flour, and process in pulses.
Heat oven to 350 degrees. Butter and flour a 9-inch springform pan. Toast pecans for 5 to 6 minutes, or until they release their aroma. Cool completely, and grind to a fine powder. Place in a bowl; combine with flour, baking powder, cinnamon, and salt. Set aside.
In the bowl of an electric mixer fitted with the whisk attachment, beat egg yolks with half the granulated sugar until mixture is thick and pale and holds a 1-second ribbon. Beat in vanilla, and set aside.
In a clean bowl, whip egg whites until they just hold stiff peaks. Add remaining sugar; beat until stiff peaks form again.
Stir 1 cup of the whites into yolk mixture. Place a quarter of remaining whites on top, and sprinkle with a quarter of the flour-nut mixture. Fold in quickly. Repeat until both flour and whites are used up. Turn batter into pan, and bake until a cake tester comes out clean, about 35 minutes. Cool in pan on a wire rack for 10 minutes, then unmold.
When cake is completely cool, invert and split into two layers with a serrated knife. Warm preserves; spoon 1 1/2 cups onto bottom layer. Replace top layer. Strain remaining preserves, and brush onto sides. Decorate cake with confectioners' sugar. Note: To make a chunkier preserve filling, simmer 1/2 cup dried apricots cut in pieces in water until soft, and add to warm preserves.