In the bowl of a stand mixer fitted with a paddle attachment or in a large bowl with a hand mixer, beat together the butter, brown sugar, and granulated sugar until light and fluffy, about 3 to 6 minutes. Add in the egg and egg yolk, one at a time. Then beat in the vanilla until just combined. Scrape down the sides of the mixing bowl and give it one final mix.
3/4 cup butter, 3/4 cup brown sugar, 1/4 cup granulated sugar, 1 egg, 1 egg yolk, 1 1/2 teaspoons vanilla extract