Preheat oven to 400°F.
In a medium sized mixing bowl, combine the flour, sugar salt, baking powder and baking soda. Give that a good whisk so it's mixed really well.
Cut the butter in 1/2 Tablespoon pats and add it to the flour mixture. Using a pastry cutter or 2 dinner knives, cut the butter into the flour mixture until the butter is about the size of peas.
Stir in the chocolate chips.
In a large mixing bowl, pour the sourdough starter, cream or milk, and the vanilla extract. Whisk those together until thoroughly mixed.
Now take the dry ingredients and add them to the sourdough mixture.
Use a spoon or your hands to combine the two. Make sure it's well combined, but don't over mix or the scones will be tough. The will not be a sticky dough. It will be a little dry and crumbly.
Press the dough in to a ball and put it on a clean counter top. It won't need a floured surface. Press into a circle about 8 inches around and about 1/2 inch thick.
Using your bench scraper or a sharp knife, cut the round into 8 wedges.
Put your chocolate chip sourdough scones on a baking stone or a greased or parchment paper lined baking sheet.
In a little bowl or coffee mug, whisk the heavy cream or milk and the sugar together until it's mixed. The sugar won't be dissolved completely.
With a pastry brush, brush the glaze mixture over the tops of the scones.
Bake for 20 to 25 minutes or until golden brown.
If you have any glaze left over, brush it over them while they are still hot.