Cut the butter into chunks and put in a deep skillet or saucepan. Stainless steel is best — don’t use dark colored or nonstick.
Turn to medium and melt and cook the butter until it turns brown and becomes fragrant and nutty. When it is well browned, turn off the heat and immediately add the butter to a large mixing bowl.
Let cool for 5 minutes and add the sugar, eggs, and vanilla. Stir until combined.
In a separate bowl, whisk together the flour, oats, baking soda, and kosher salt. Add to the butter mixture and stir well.
Refrigerate your dough for 15 minutes.
Line a baking sheet with parchment and scoop the dough into 2 inch balls about 2 inches apart. Flatten slightly and sprinkle with coarse salt if using.
Bake for 10-12 minutes, until cookies are browned.
Remove from oven and let cool on a wire rack before serving.