Preheat the oven to 375F, with racks in the upper and lower thirds. Line two large baking sheets with parchment paper; set aside.
In a medium bowl, whisk together the flour, baking soda, and salt; set aside.
In another bowl, beat the butter and both sugars on medium speed with an electric mixer until light and fluffy (about 3 minutes) scraping down the sides of the bowl as needed.
Add the vanilla, whole egg, and egg white, beating on low speed until well combined (about 1 minute).
Add flour mixture in two batches; mix until just combined.
Mix in chocolate.
Shape 2 heaping tablespoons of dough at a time into balls and place about 1 1/2 inches apart on prepared baking sheets.
Bake, rotating sheets halfway through, until cookies are golden brown, about 18 minutes.
Transfer parchment and cookies to a wire rack to cool completely.
Cookies can be kept in an airtight container at room temperature for up to 4 days.