Preheat oven to 400°F. Line a baking sheet with parchment paper.
In a large bowl, combine the flour, baking powder, baking soda, salt, and sugar.
Grate the frozen butter on the large holes of a box grater, then cut the butter into the flour mixture with a pastry cutter. If it's warm in your kitchen, I recommend popping the bowl in the freezer for 10-15 minutes to keep the butter really cold.
In a separate bowl, whisk together the cream, egg, and vanilla extract. Add to the flour mixture with the chocolate chips, stirring with a fork or spatula to moisten the dry ingredients into a very shaggy dough.
Turn out the dough onto the parchment-lined baking sheet. Use the parchment paper to lift and press the scone dough together. It's a sort of modified folding and kneading and made much easier with the parchment paper, plus this helps avoid too much heat from your hands softening the butter.
Pat the dough into a circle approximately 8-inches in diameter. Use a bench scraper to divide the dough into 8 triangle-shaped scones, then space them out on the parchment paper.
Brush the tops of each scone with cream, then sprinkle with the coarse sugar.
Bake for 20-22 minutes until golden brown on top. Take care not to overbake so you don't end up with dry scones.
Make the glaze by whisking the powdered sugar, cream, vanilla, and salt together in a bowl, then drizzle over the cooled scones.