In a mixing bowl, cream together the softened butter and brown sugar using a wooden spoon, hand mixer or stand mixer. Add the granulated sugar, egg and egg yolk, and vanilla, mixing to combine between each addition.
In a separate bowl, combine the all-purpose flour, baking soda, baking powder and salt. Stir to combine. Add the dry mixture to the wet ingredients and stir to mostly combine.
Add both kinds of chocolate chips, and mix until fully combined but do not overmix.
Cover and chill dough at least 2hrs, or overnight.
When ready to bake, preheat oven to 350°F, and line a baking sheet with parchment paper.
Scoop cookie dough with a spoon, cookie scoop, or #40 disher, and roll into balls approximately 1in in diameter. Place dough balls on the parchment-lined baking sheets about 2in apart. Bake cookies until they are light golden brown around the edges, and the centers look soft, but just set.
**If desired, swirl the freshly baked cookies with a pastry ring or biscuit cutter to gather the cookie together with perfectly rounded edges.
Allow cookies to cool on the sheet pan for about 5min before transferring to a cooling rack to cool completely.
Store cooled cookies in an airtight container for 3-5 days at room temperature. See Recipe Notes for tips on freezing.