Combine softened butter and sugars in a large bowl. Beat at medium speed with an electric hand mixer for about 2 minutes.
Add the egg, vanilla, and sourdough discard. Beat just until combined.
Add the flour, baking powder, baking soda, salt, and chocolate chips. (I like to reserve about 1/2 cup for the tops of the cookies.) Stir until there are no streaks of flour.
Cover the dough or wrap it in plastic wrap. Chill for at least 8 hours, or overnight.
Roll dough into 1 1/4" - 1 1/2" balls. I like to use a cookie scoop to make sure my cookies are all the same size. Place in the refrigerator while you preheat your oven to 375°.
Line cookie sheet(s) with silicone liners or parchment paper.
Bake at 375 degrees for 10-12 minutes, or until barely golden brown around the edges. Don't overbake or they won't be soft.
Immediately press a few chocolate chips on top of each hot cookie.
Let cookies sit on the pan for 2-3 minutes, then transfer with a metal spatula to a wire rack to cool.
Notes
I like to use half milk chocolate and half semi-sweet chocolate chips, but you can use any kind you prefer.
You can store cookies in an air-tight container for up to a week. They also freeze well.