Preheat oven to 350°F (175°C).

Combine brown rice flour, tapioca flour, toasted almonds, dried apricots, cinnamon, baking powder, nutmeg, and salt in a food processor.

Process until finely chopped, about 1 minute.

In a large bowl, beat egg yolks and 1/3 cup granulated sugar until thick and pale.

In a separate large bowl, beat egg whites until stiff peaks form.

Gradually add remaining 1/3 cup granulated sugar and vanilla to the egg whites, beating until stiff peaks form.

Gently fold flour mixture and one-third of egg white mixture into the egg yolk mixture.

Fold in remaining egg white mixture, being careful not to deflate the batter.

Pour batter into a 9-inch springform pan coated with cooking spray and dusted with tapioca flour.

Bake for 35-38 minutes, or until a toothpick inserted into the center comes out clean.

Cool in pan for 15 minutes before removing from pan to cool completely.

Beat cream cheese and butter until light and fluffy.

Gradually add powdered sugar, beating until smooth.

Beat in vanilla extract.

Cut cake in half horizontally.

Spread apricot preserves over the cut side of the bottom layer.

Top with the remaining cake layer.

Spread cream cheese mixture over the top of the cake.

Sprinkle with sliced almonds and chopped apricots.

Cover loosely with plastic wrap and refrigerate.