Preheat the oven to 375 degrees F. Line a baking sheet with parchment paper.
In a large bowl, combine the flour, sugar, baking powder, and salt. Using a food processor or pastry cutter, cut in the butter until the mixture is crumbly. Add the cream cheese, stirring to combine, then add the heavy cream, stirring just until the dry ingredients are moistened.
On a lightly floured surface, roll out the dough to 3/4-inch thickness. Cut the dough with a 2 1/2-inch round cutter, rerolling as necessary. Arrange the shortcakes on the prepared baking sheet and bake until lightly browned, about 13 to 15 minutes. Remove from the oven and cool completely before serving.