Preheat oven to 425°F (220°C). Line a baking sheet with parchment paper or a silicone liner.
Whisk together the flour, baking powder, and salt.
Add the cream cheese and butter. Mix with a pastry blender, a fork, or your fingers just until combined.
Add the milk, and continue mixing just until the dough comes together.
Transfer the dough to a lightly floured surface. Use your hands to pat the dough to about a 3/4-inch thickness.
Use a 2 1/2-inch square biscuit cutter to cut out the biscuits. After you've cut out as many biscuits as you can, gather the dough once more and cut out the remaining biscuits.
Transfer the biscuits to the prepared pan. Place them close together for softer sides or further apart for crisper sides.
Bake 14 to 16 minutes, or until lightly browned.
To make the filling:
Combine the cherries, sugar, water, and cornstarch in a heavy saucepan.
Cook over medium heat, stirring frequently, until the mixture comes to a boil. Continue cooking 3 or 4 minutes, or until the mixture has thickened to the desired consistency.
Remove the mixture from the heat, and stir in the vanilla. Set aside to cool.
To assemble the shortcakes:
Split the biscuits in half, placing the bottom halves with the cut side up.
Dollop whipped cream on top of each biscuit half. Spoon some of the cherry mixture over the whipped cream.
Top with the top halves of the biscuits. Add more whipped cream and cherries if desired.
Notes
Adjust the sugar to your tastes and according to the sweetness of the cherries you're using.
You can use a different size biscuit cutter if you like. Keep in mind that you'll get a different yield.
You'll need about 1 to 1 & 1/2 cups of whipped cream, depending on how much you want to add to your shortcakes.
The components of these shortcakes can be made in advance and then assembled when you're ready to serve. You'll need to refrigerate the cherries and whipped cream. The cherries and their sauce can best be reheated over low heat on the stovetop, adding a bit more water if necessary to get the consistency as you want.