In a large bowl, combine 1½ pounds sliced strawberries with 2 tablespoons granulated sugar. Stir to coat, cover, and refrigerate while you prepare the shortcakes.
In the bowl of a food processor, combine 3 cups all-purpose flour, 1/4 cup granulated sugar, 1½ tablespoons baking powder, 1/2 teaspoon baking soda, and 1 teaspoon salt. Pulse a few times to combine.
Add 3/4 cup cold cubed butter and pulse until the mixture resembles coarse crumbs with small pieces of butter remaining.
Transfer the mixture to a large mixing bowl. Add 1 cup heavy whipping cream and 1 teaspoon vanilla extract. Stir just until a shaggy dough forms.
Turn the dough onto a lightly floured surface and gently knead it a few times until it comes together. Do not overwork the dough.
Roll the dough into a 9 x 12-inch rectangle about 3/4-inch thick.
Using a 2¾ to 3-inch biscuit cutter, cut out 10 to 12 biscuits. Gather and gently reroll the scraps as needed to cut additional biscuits.
Place the biscuits on a parchment paper-lined baking sheet. Refrigerate for 20 to 30 minutes while the oven preheats to 425°F.
Brush the tops of the biscuits with the remaining 2 tablespoons heavy whipping cream and sprinkle with the remaining 2 tablespoons granulated sugar.
Brush the top of the biscuits with 2 tablespoons of heavy cream and sprinkle the additional granulated sugar on top.
Bake for 15 to 20 minutes, or until the tops are golden brown. Transfer the biscuits to a wire rack and cool completely.
Chill a mixing bowl and beaters in the freezer for about 15 minutes.
Add 2 cups heavy whipping cream, 1/4 cup granulated sugar, and 1 teaspoon vanilla extract to the chilled bowl.
Beat with an electric mixer until stiff peaks form.
Slice each biscuit in half horizontally.
Spoon strawberries onto the bottom half of each biscuit, followed by a generous dollop of whipped cream.
Place the top half of the biscuit over the filling and finish with additional strawberries and whipped cream. Serve immediately.