Preheat the oven to 425°F and line a large baking sheet with parchment paper and set aside.
Add 2½ cups cake flour , ⅓ cup granulated sugar, 1 tablespoon baking powder, and ½ teaspoon salt to an 8-cup (or larger) food processor and pulse for 15 seconds.
2½ cups cake flour, ⅓ cup granulated sugar, 1 tablespoon baking powder, ½ teaspoon salt
Cut ¾ cup cold unsalted butter into cubes, add it to the food processor, and pulse until the mixture turns sandy.
¾ cup cold unsalted butter
Add in 3 ounces cold heavy cream, 1 cold large egg, and 1 tablespoon vanilla bean paste and pulse until a dough forms and just begins to pull completely away from the sides while mixing.
3 ounces cold heavy cream, 1 cold large egg, 1 tablespoon vanilla bean paste
Divide the dough into 3 even portions (about 8.6 ounces each). Run your hands under cold water and pat dry, then roughly shape the portions of dough into balls using your hand and the counter, then both hands (there will be cracks in the dough. We want to handle the dough as little as possible and keep it as cold as possible.
Place a ball of dough on a piece of parchment paper, then place another piece over the top of the ball. Use a rolling pin to roll the ball into a circular disc that is 5 inches in diameter and about ¾-inch thick. Gently use your hands to press in the sides to even out and fill in the cracks a bit - do this by holding your hand palms to the dough with pinkies on the table and thumbs to the sky.
Use a bench scraper or large chef knife to slice the disc into 6 triangles. Place the scones on the prepared baking sheet at least 1 inch apart. Repeat the last two steps with the remaining balls of dough.
Bake for 9 to 11 minutes, the bottom edges should be golden brown and the tops firm to the touch.
Allow the scones to cool on the pan for a few minutes before transferring them to a wire rack to cool completely, about 1 hour.
Once cooled, prepare the icing by whisking together the 1 cup powdered sugar, 3 ounces heavy cream, and 1 tablespoon vanilla bean paste - it will be thick.
1 cup powdered sugar, 1 tablespoon vanilla bean paste, 3 ounces heavy cream
Dip the scones or drizzle them with the icing and place them on a piece of parchment paper for the icing to set.