Preheat the oven to 350ºF. Separate the egg whites from the yolks. Beat the whites to a stiff, glossy foam. Toward the end of whisking, add sugar, spoon by spoon, beating a little after each addition. Add the egg yolks one at a time, still beating. Sift gluten-free flour and almond flour into the egg mixture and gently fold in using a spatula to combine the ingredients.
Line the bottom of a 9-inch cake pan with a removable bottom with parchment paper. Divide the batter into 3 equal parts, so you can work in batches. Gently spoon one-third of the batter into the cake pan, leveling it out. Bake at 350º F for about 25 minutes. After baking, remove from the oven, cool to room temperature. Remove from the pan, cut off the outer browned crust of the sponge cake with a long, sharp knife and bake two more sponge cakes in the same way. If you have 3 identical cake pans, you can bake all the cakes at the same time.
Make the cream. Place the heavy cream in the bowl of a mixer and beat for 2 minutes. Gradually add mascarpone, white chocolate, and vanilla extract, mix until well combined and thick.
Place the first sponge cake on a platter. Arrange one-fourth of the cream on top, level it out. On the cream, arrange sliced strawberries. Cover with the second cake and press very lightly, just to combine the layers. Cover with another portion of cream. Level it out. Arrange the strawberry slices on the cream and cover with the last sponge cake. Spread the top and edges of the cake with the remaining cream, decorate with strawberries and fresh mint. Store in the refrigerator for up to 24 hours.