Preheat the oven to 350 degrees F. Butter and flour a 9-inch cake pan.
Combine the whole almonds and 1/4 cup pine nuts in a food processor. Pulse the machine until the nuts are finely ground. Transfer the nuts to a medium bowl. Add the flour, baking powder, and salt. Stir to combine and set aside.
In a medium bowl, using an electric mixer beat the eggs and the sugar until the mixture becomes thick and pale yellow. Add the butter, and milk. Stir in the almond extract and apricots. Gently stir in the dry ingredients. Pour the batter into the prepared cake pan. Sprinkle the top of the cake with sliced almonds and remaining 1/4 cup pine nuts. Bake until the cake is cooked and a toothpick comes out clean, about 50 to 55 minutes. Let the cake cool on a wire rack. Use a knife to loosen the edges. Turn the cake out, slice, and serve.