Brown the butter in a light skillet over medium heat until nutty and amber; cool 10 minutes.
Whisk cooled brown butter with both sugars, then beat in eggs and vanilla until smooth.
Stir together flour, baking soda, cinnamon, and salt; fold into wet mixture.
Mix in oats and raisins until evenly distributed.
Scoop 2-tablespoon mounds onto a lined baking sheet, 2 inches apart.
Bake at 350°F (175°C) for 10–12 minutes until edges are set and centers look slightly soft.
Cool 5 minutes on the sheet, then transfer to a rack to finish cooling.