In a big mixing bowl, mix together 2 cups of all-purpose flour, 1/3 cup of white sugar, 1 tablespoon of baking powder, and 1/4 teaspoon of salt.
Grate 1/2 cup of chilled butter into the flour mixture or cut the butter into small pieces and use a pastry cutter to combine until the mixture looks like coarse crumbs.
Add 1 cup of heavy cream, 1 large egg, 1 teaspoon of vanilla extract, and 1 cup of mini chocolate chips to the mixture. Stir until everything is well combined and no dry flour remains.
Lightly flour a clean surface. Move the dough onto it and shape it into a large ball with your hands.
Flatten the dough into a 2-inch thick disc. Cut the disc into 8 wedges using a butter knife.
Place the scones on an ungreased baking sheet and brush the tops with 2 tablespoons of heavy cream.
Bake at 425°F for 12-15 minutes, until the tops are golden brown.
While the scones are baking, prepare the icing. In a small bowl, mix 1 cup of powdered sugar with 2 tablespoons of milk and 1 teaspoon of vanilla extract until smooth.
Once the scones are done, let them cool on the baking sheet on a wire rack. Drizzle the icing over the warm scones using a spoon.