Preheat the oven to 350 degrees F. and butter and flour a 9 inch springform pan.
In a food processor or blender, chop the whole almonds until mostly ground. You want them ground pretty well, but not as fine as flour.
In a mixing bowl, beat the heavy cream until stiff peaks form to make whipped cream. Place in the fridge.
In a separate bowl, beat the eggs, sugar, and almond extract for 5-10 minutes, until fluffy and lighter in color.
Fold in the ground almonds, flour, baking powder, and salt until smooth.
Gently fold in the chilled whipped cream using a spatula until smooth. Be careful not to deflate the batter.
Pour the batter into the prepared pan.
Top with slivered almonds and sprinkle with sugar.
Bake for 38-45 minutes, until the edges brown and a toothpick inserted in the middle comes out clean.
Allow the cake to cool for 10 minutes, then release it from the pan.
Top with powdered sugar if desired.