Preheat oven to 375 F (190C) and line a cookie sheet with parchment paper.
In large bowl, combine flour, sugar, baking powder and salt.
Thoroughly cut in butter (I prefer to freeze the butter, grate it using a box grater, and then cut it in that way. This method yields the flakiest scones, but is not mandatory -- you can use cold butter cut in with a pastry cutter).
Measure out heavy cream in measuring cup and add vanilla extract. Stir gently.
Carefully stir heavy cream/vanilla mixture into flour mixture. You do not want to over-mix, but due to the amount of dry ingredients it may be tricky to well incorporate the liquid and the dry mixes. You may briefly use a KitchenAid or electric mixer on a low setting to help coax the dough to cling together.
Once dough is beginning to cling together, add chocolate chips, stir briefly, and then transfer to a very lightly floured surface
lightly knead the dough and chocolate chips together until you are able to form a ball.
Break the dough into 4 even pieces and round each one out into a disk about 5" wide.
Cut each into 8 wedges and transfer to cookie sheet.
Bake on 375F (190C) for 14-16 minutes.
While the scones cool, prepare your glaze by whisking together milk, vanilla extract, and powdered sugar. Start with 1 cup powdered sugar, and if it still seems too runny you may increase the sugar amount.
Once scones are cooled, dip, drizzle or spoon the glaze lightly over the top of each scone. Allow it to sit and harden before serving.