In a small pan, brown the butter over medium heat. Carefully watch the butter so that it doesn't burn, letting it turn to a brown color and give off a nutty aroma. Once butter is browned, let it cool then refrigerate it to turn the butter back into a solid form but not totally cold (this may take about 30 minutes)
Preheat oven to 350 degrees.
In a large mixing bowl, combine oats, flour, baking powder and salt.
Using a stand mixer combine the browned butter and sugars until they are light and fluffy. Add in the eggs one at a time. Stir in the vanilla, then gradually add in the dry mixture. Once combined, stir in the butterscotch chips.
Line a cookie sheet with parchment or a silt pat and bake cookies at 350 for 8-10 minutes or until golden brown. Remove from oven and let cool completely before making into ice cream sandwiches.