Start by browning the butter. In a medium saucepan, melt the unsalted butter over medium heat until it turns golden brown and has a nutty aroma, about 5-7 minutes. Let it cool slightly.
In a separate bowl, whisk together the all-purpose flour, baking soda, salt, and ground cinnamon.
In a large mixing bowl, combine the browned butter, brown sugar, and granulated sugar. Mix well. Add the eggs one at a time, followed by the vanilla extract.
Gradually add the dry ingredients to the wet mixture. Stir gently until just combined.
Fold in the rolled oats and butterscotch chips until the dough is thick and chunky.
Chill the dough in the refrigerator for at least 30 minutes for better flavor and texture.
Preheat your oven to 350°F (175°C). Drop mounds of dough onto a prepared baking sheet, leaving space between each cookie. Bake for 10-12 minutes.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack.