Place 3/4 cup (1 1/2 sticks) unsalted butter in a large skillet set over medium heat. Cook until the milk solids in the butter turn golden brown. Pour the browned butter into a small bowl.
In the bowl of a food processor, combine congealed butter, 1/2 cup packed light brown sugar, 1/2 cup granulated sugar, 1 cup all-purpose flour, 1/2 tsp baking soda, 1/4 tsp salt, and 2 large eggs.
Bake until the cookies are deep golden brown, 11-13 minutes, switching the baking sheets top to bottom and back to front halfway through. Transfer the cookies to a cooling rack. They will become crisp as they cool.