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For the Shortcakes: Remove the yolks from the hard boiled eggs. Press the yolks through a sieve or chop very finely. Whisk together white rice flour, potato starch, 1/4 cup of the sugar, baking powder, and xanthan gum in a large bowl. Add cubed butter and, using either your hands or a pastry cutter, cut into flour mixture until pea-sized pieces form. Add egg yolks and continue cutting until flour mixture resembles coarse crumbs. Stir in heavy cream with a wooden spoon until incorporated. Let dough stand for 5 minutes.
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Generously dust work surface with white rice flour. Turn dough onto work surface and dust with more white rice flour. Gently knead the dough a few times, then pat into a large rectangle, about 1 inch thick. Using a 2-inch round cutter, cut out four dough rounds. Gather up dough scraps, pat into a 1-inch-thick rectangle, and cut out 4 more dough rounds; discard remaining dough scraps. Place dough rounds on a parchment-lined baking sheet and brush the tops with remaining 1 tablespoon melted butter. Sprinkle remaining 1 tablespoon granulated sugar on top. Cover with plastic wrap and refrigerate for 1 hour.
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For the Topping: Stir together strawberries, 1/4 cup granulated sugar, and 1 teaspoon vanilla extract. Using the back of a fork, gently mash a few of the sliced strawberries. Allow strawberries to stand for 1 hour.
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In medium bowl, whip heavy cream until soft peaks form. Add remaining 1 tablespoon granulated sugar and 1 teaspoon vanilla extract, and beat until stiff peaks form.
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Adjust oven rack to center position and preheat oven to 350°F. Remove plastic wrap from baking sheet and bake shortcakes until edges just turn golden brown, about 12 minutes. Let shortcakes cool on baking sheet for five minutes, then transfer to a wire rack. Serve shortcakes warm or at room temperature, topping with macerated strawberries and whipped cream.