In a medium saucepan, melt the unsalted butter over medium heat. Cook until it turns a deep golden brown and develops a nutty aroma, about 5-7 minutes. Let it cool slightly.
In a large mixing bowl, whisk together the all-purpose flour, baking soda, salt, and ground cinnamon.
In a separate bowl, combine the brown sugar and granulated sugar. Add the slightly cooled brown butter and mix well. Add the eggs and vanilla extract, whisking until smooth.
Gradually add the dry mixture to the wet mixture, stirring just until combined.
Fold in the rolled oats and butterscotch chips using a spatula.
Cover the bowl with plastic wrap and refrigerate the dough for at least 30 minutes.
Preheat your oven to 350°F (175°C) and line your baking sheets with parchment paper.
Drop rounded balls of dough onto the prepared baking sheets, spacing them about 2 inches apart. Sprinkle a pinch of sea salt on each ball if desired.
Bake the cookies for 10-12 minutes until the edges are lightly golden and the centers look set but soft.
Cool on the baking sheets for about 5 minutes before transferring to a cooling rack to cool completely.
