Preheat the oven to 400˚F. Line a large baking sheet with parchment paper.
In a large bowl, whisk together the all-purpose flour, almond flour, baking powder and salt. Using the large holes of a cheese grater, grate the butter over the top of the dry mixture (alternatively, use a box grater to grate the butter onto a piece of wax or parchment paper, then sprinkle the butter over the flour). Place the bowl in the freezer for 10 minutes to chill.
In a small bowl, wish one of the eggs with 1 teaspoon of water. Set aside (this will be the egg wash for later).
In a separate bowl, whisk the remaining egg with the sugar, milk and almond extract until smooth.
Take the bowl out of the freezer, and toss the butter with the flour mixture until evenly incorporated. Make a well in the center of the bowl and pour in the wet ingredients. Slowly work the dry ingredients into the wet ingredients until incorporated, being careful not to overwork the dough (it should look shaggy and a bit floury).
Turn the dough out onto a lightly floured piece of parchment paper. Using your hands, gently press the dough into a 1-inch thick square (about 6 ½ inches wide). Cut the dough into 9 squares, and transfer them to the baking sheet. Do Ahead: The uncooked shortcakes can be wrapped in wax paper and frozen (in a single layer) in an airtight container or ziptop bag. When ready to bake, proceed as directed—don’t defrost.
Brush the shortcakes lightly with the egg wash (you won’t need it all), and sprinkle them with the turbinado sugar and sliced almonds. Bake until golden brown, about 15-17 minutes. Let cool.
Carefully cut the shortcakes in half horizontally (a small serrated knife works well), and fill them with sliced strawberries and whipped cream. Alternatively, serve the shortcakes on their own as scones!