Preheat the oven to 325 degrees and position the rack to the center of the oven. Line the bottom of a 9-inch cake pan with a round of parchment paper, or butter and dust it lightly with flour, tapping out any excess.
With an electric mixer, beat together the sugar and almond paste until the paste is finely broken up (the sugar crystals help break the paste into pieces--so don't add the butter yet!).
Now add the butter and beat for a few minutes until light and fluffy. In a separate bowl stir together the eggs with a fork then dribble it into the batter as you beat. Add the vanilla.
Mix together the flour, baking powder and salt with a whisk. Stir the dry ingredients into the batter until just incorporated.
Transfer the batter into the prepared cake pan and bake about 1 hour, or until a toothpick inserted into the center comes out clean. The baking time may take a bit longer due to the variation in different brands of almond paste.