In a saucepan, melt butter over low heat, then set aside to cool for at least five minutes.
In a large mixing bowl, combined cooled butter with sugars and beat with an electric mixer for two minutes. Then add egg and yolk, one at a time, mixing after each addition. Add in vanilla and mix until combined.
In a separate bowl, combine flour, baking soda and salt. Mix well. Add half of the dry ingredients to the wet ingredients, and stir by hand to combine. Add remaining dry ingredients, and stir to combine, but do not overmix. Fold in chocolate chips, stirring until just mixed in.
Tightly cover dough and chill in refrigerator for at least one hour, and up to 24 hours.
When ready to bake, preheat oven to 375 degrees F. Scoop and drop dough, approximately a heaping tablespoon each, onto an ungreased cookie sheet. Bake for 8-10 minutes, or until the edges just start to brown. Remove from oven and allow to cool on baking sheet for two minutes, then transfer to a wire cooling rack to finish cooling.