In a medium bowl, whisk the melted butter, brown sugar and granulated sugar together until no brown sugar lumps remain. Whisk in the egg, then the egg yolk and lastly the vanilla extract.
Pour the wet ingredients into the dry ingredients and mix together with a large spoon or rubber spatula. Add the chocolate chips or chocolate chunks.
Cover the dough and chill in the refrigerator for 2-3 hours or overnight. Chilling is mandatory. I highly recommend chilling the cookie dough overnight for less spreading.
Preheat oven to 325°F. Line two large baking sheets with parchment paper or silicone baking mats.
Roll the dough into balls, about 1 tablespoon of dough each. Roll the cookie dough balls to be taller rather than wide. This will allow the cookies to be on the thick side. Place 12 balls of dough onto each cookie sheet.
Bake the cookies for 11 minutes. The cookies will look under baked. They will continue to bake on the cookie sheet. Allow to cool on the cookie sheet for 10 minutes before transferring to a wire rack to cool completely.
You can make the cookie dough and chill it in the refrigerator for up to 2-3 days. Allow to come to room temperature then continue with step 4.
Cookies stay fresh covered at room temperature for up to 1 week or freeze cookies up to 3 months.