Line a baking sheet with parchment paper.
To make the dough: In the bowl of a stand mixer fitted with the paddle attachment, add the flour, cane sugar, baking powder, and sea salt. Mix on low to for 2 to 3 rotations to combine the dry ingredients.
Using a large grater, grate the butter and add to the flour mixture. Don’t mix yet.
Add the sourdough discard, buttermilk, egg, and vanilla extract, and mix on low to combine. Add the chocolate chips and mix to combine. You’ll have to scrape the bowl to help combine the dry ingredients, and I find it’s easier to finish combining with your hands.
Using your hands, form the dough into a rectangle that is about 7 x 5-inches in diameter. Using a sharp knife, cut into 6 square pieces (cut down the middle lengthwise, and then in three). Separate the pieces so they are spaced evenly apart.
Place the baking sheet in the fridge for 30 minutes. Preheat the oven to 400°F.
Bake for 20 to 24 minutes or until lightly golden brown on the bottoms. Allow to cool completely on the baking sheet.
Melt the additional chocolate chip, either using a double boiler, or in a microwave safe bowl doing 30 intervals, stirring between each one.
Drizzle the melted chocolate over the tops of the scones.
Store in a cool dry place for up to 3 days.