"Brown butter adds extra deliciousness to these oatmeal chocolate cookies. Honestly, they are the best cookies I've eaten (store-bought or homemade)! Prepare the brown butter in advance because it will have to cool completely."
Melt butter in a saucepan over medium heat; cook, swirling the pan frequently, until the butter is browned, about 5 minutes. Pour browned butter into a bowl and set aside to cool.
Preheat oven to 325 degrees F (168 degrees C).
Beat browned butter, brown sugar, and white sugar together in a large bowl until smooth and creamy. Beat one egg into the butter mixture until smooth; add second egg and vanilla extract and beat again until smooth and uniform in color.
Mix oats, flour, baking soda, and salt in a bowl; add to the browned butter mixture and stir to get a cookie dough. Stir chocolate chips into the dough. Drop dough by heaping teaspoonful onto baking sheets.
Bake in preheated oven until edges and bottoms are golden brown, about 12 minutes. Cool on sheets for 10 minutes before transferring to wire cooling racks to cool completely.