In a large mixing bowl or in the bowl of a stand mixer with a paddle attachment, cream the butter and sugars together on medium speed for 3 minutes.
Add the egg yolk and vanilla and mix until combined and creamy
Stir in the sourdough starter for about 1 minute until combined
Stir the flour and salt and mix on low speed until incorporated, about 30-60 seconds.
Fold in the chocolate.
Prepare two baking sheets (lightly grease or use a silicone baking mat, I prefer not to use parchment paper to reduce waste).
Use a spoon or cookie scoop to make equal-sized cookie dough balls (about 2 tablespoons [45g]) of cookie dough, roll into even balls, and place them, 4 inches (10 cm) apart, on the prepared baking sheets.
Cover and chill for 2 hours or up to 2 days.
Preheat the oven to 375°F
Bake one sheet at a time for 10-12 minutes, or until the edges are set and golden brown with crispy edges
Remove from the oven and let cool on the cookie sheet for about 5 minutes, or until firm enough to move.
Then, transfer to a cooling rack and let cool completely.