For the scones: Preheat the oven to 350 degrees F. Line a baking sheet with parchment or a silicone baking mat.
Sift together the flour, granulated sugar, baking powder and salt in a bowl. Cut the cold butter into pats, then use a pastry cutter or 2 knives to cut the butter into the flour mixture until it resembles crumbs. Mix in the chocolate chips.
Add the cream to a pitcher, then whisk in the vanilla and egg. Pour the cream mixture into the flour mixture; stir gently with a fork just until it comes together.
Turn the dough out onto a floured surface and lightly press it together until it forms a rough rectangle (the mixture will be pretty crumbly). Use a rolling pin to roll it into about a 12-by-7-inch rectangle, 1/2 to 3/4 inch thick. Use your hands to help with the forming if necessary. Use a knife to trim into a symmetrical rectangle, then cut the rectangle into 12 symmetrical squares/rectangles. Next, cut each square/rectangle in half diagonally, to form 2 triangles. Transfer to the prepared baking sheet.
Bake until the scones are light brown--not golden--about 18 minutes. Allow to cool for 15 minutes on the baking sheet, then transfer to a cooling rack to cool completely.
For the glaze: Add the milk and vanilla to a pitcher and mix together. Mix the confectioners' sugar and salt in a bowl. Add the milk mixture and stir or whisk until completely smooth. Add more confectioners' sugar or milk if necessary to get the consistency the right thickness.
One at a time, carefully dunk each cooled scone in the glaze, turning it over if necessary to completely coat. Put on a cooling rack over a baking sheet. Allow the glaze to set completely, about 1 hour. The scones will keep several days if glazed.