Melt the butter in a small saucepan over low heat or in the microwave in short bursts. Let it cool for 5 to 10 minutes, until warm but not hot.
In a large bowl, whisk the cooled butter with the brown sugar and granulated sugar until smooth and glossy.
Add the egg, egg yolk and vanilla and whisk for about a minute, until the mixture looks thick and pale.
Sprinkle the flour, baking soda and salt over the bowl. Fold with a spatula until just combined, with no dry streaks left.
Fold in the chocolate chips.
Cover the bowl and refrigerate the dough for 30 minutes, or up to 24 hours.
Heat the oven to 350°F (175°C) and line two baking sheets with parchment paper.
Scoop the dough into balls of about 2 tablespoons each and place them 2 inches apart on the sheets, about 8 per sheet.
Bake one sheet at a time for 10 to 12 minutes, until the edges are golden and the centers still look slightly soft and puffy.
Sprinkle with flaky salt if you like. Let the cookies rest on the sheet for 5 minutes, then move them to a wire rack.
