Hull and chop the strawberries into small pieces. In a bowl, mash half of them with a fork. Add the remaining chopped strawberries into the bowl with mashed berries. Add ¼ cup sugar and lime juice.
In another bowl, roughly mash the blueberries with a fork in a way that some are burst and some remain intact. So a rough mash. Add two teaspoons sugar. Mix.
Put both the bowls in the refrigerator until we are ready to assemble our shortcakes.
Preheat the oven to 425 degrees F or 220 degrees C. Line a cookie sheet with parchment.
In the bowl of your stand mixer (See notes), add all the dry ingredients, i.e. flours, salt, sugar, baking powder, and baking soda.
With the paddle attachment mix them together.
In a glass measuring cup, take 1 cup buttermilk and add vanilla and egg to it. Whisk to combine. These are your wet ingredients.
To the mixed dry ingredients in the stand mixer bowl, add chopped cold butter pieces. Mix until the mixture resembling peas/crumbly texture is formed. See notes
To this now slowly add the wet ingredients and mix on medium speed until the dough just holds together.
Sprinkle some flour on a rolling surface (could be your kitchen counter) and dump the dough out. You might have to knead it lightly and then pat it until it is almost ¾ of an inch thick. Using a medium size biscuit cutter dipped in flour (see notes) cut into circles.
You might have dough scraps left after cutting first few biscuits. Pat the scraps together and cut more biscuits. Repeat until all the dough is used up. I got 14 shortcakes from this dough.
Place the biscuits on the prepared cookie sheet, brush the tops with milk, and sprinkle each shortcake with turbinado sugar, if desired.
Bake for 10 to 12 minutes, until the tops are golden brown. Remove them from the oven and let cool completely.