Preheat the oven to 425 degrees F and line a baking sheet with parchment paper.

In a large mixing bowl, whisk together the flour, sugar, baking powder, and salt until evenly combined.

Add the cold butter cubes and cold cream cheese cubes to the flour mixture. Use a pastry cutter, fork, or fingertips to work the butter and cream cheese into the flour until the mixture appears crumbly, with small pea-sized pieces throughout.

Pour in the cold buttermilk and vanilla extract, then gently stir until the dough just begins to come together, avoiding overmixing.

Turn the mixture onto a lightly floured surface and gently press it into a thick rectangle. Fold the dough over itself once or twice, patting it into a rectangle about 1 inch thick.

Cut the dough into squares using a sharp knife or biscuit cutter and place on the prepared baking sheet with space between each biscuit.

Brush the tops with heavy cream and sprinkle with coarse sugar if desired.

Bake for 15 to 18 minutes, or until the biscuits are puffed, golden brown on top, and cooked through.

Let them cool for a few minutes before glazing.

To create the optional glaze, whisk together powdered sugar, milk or heavy cream, and vanilla extract until smooth, then drizzle it over the warm biscuits just before serving.