Mix the butter and sugar: In a large mixing bowl, gently stir together the granulated sugar and room-temperature butter with a sturdy spatula or electric mixer on low until just combined.
Add wet ingredients: Stir in the molasses, vanilla extract, sourdough discard, egg, and egg yolk until fully combined.
Incorporate dry ingredients: Slowly add in the flour, baking soda, and sea salt. Stir until a tacky dough forms.
Fold in chocolate chips: Gently fold in the semi-sweet chocolate chips until distributed throughout the dough.
Refrigerate the dough: Cover the bowl and chill the dough in the refrigerator for 2 to 24 hours. Chilling allows the butter to firm up, reducing excessive spreading during baking.
Preheat the oven: Preheat your oven to 350°F.
Shape the dough: Scoop and roll the chilled dough into 2-inch balls. Place them 3 inches apart on a baking sheet.
Cool the cookies: Cook the cookies for 10-12 minutes until they are light golden brown around the edges. Allow the cookies to rest on the baking sheet for at least 10 minutes before moving them to a cooling rack to fully cool.