Melt butter over medium heat in a stainless steel saucepan (this is important so you can tell when the butter has browned.) Whisk frequently for several minutes. When you start to smell the nutty aroma of the butter browning, and see small browned bits at the bottom of the pan, immediately remove pan from heat and carefully pour browned butter into a large mixing bowl.
Preheat the oven to 350 degrees F (175 degrees C). Line a baking sheet with parchment paper.
Whisk flour, oats, salt, and baking soda together in a bowl until well combined; set aside.
Add both sugars to the bowl with the browned butter and beat with an electric mixer until smooth. Add eggs, 1 at a time, beating after each addition. Add vanilla bean paste and beat for 1 more minute. Add flour mixture in 3 batches, mixing well after each addition. Stir in chocolate chips.
Using a 1 1/2 tablespoon spring-hinged scoop, scoop out dough and place 2 inches apart on the prepared baking sheet.
Bake in the preheated oven until lightly browned, about 13 minutes. Transfer cookies to wire racks and allow to cool.