Cream together butter and both types of sugars in a stand mixer or a bowl with a hand held mixer. Beat on high for 3-5 minutes or until paler and creamy.
Scrape down the bowl before adding vanilla and egg. Continue to mix thoroughly on high for a few minutes.
Using a sifter over the butter mixture, sift flour, baking soda, and salt over the wet ingredients.
Mix on low until the dough comes together.
Scrape down the sides and bottom before adding the cup of butterscotch chips and chopped graham crackers. Mix on low just until they are mixed into the dough.
Scoop 12 portions of dough with a 3 ounce cookie scoop onto a parchment lined baking tray.
To avoid spreading in the oven, I recommend chilling your dough in your fridge for 2 hours and up to overnight.
Bake cookies at 375*F for 10-12 minutes. The edges should be golden brown and they will slightly spread so don't overcrowd your baking sheet. I bake 6-9 at a time.
Sprinkle with as much or as little sea salt as you like on top after you take them out of the oven.
Cool on pan for 10 minutes before transferring to wire rack to finish cooling.
While the cookies cool, I prepare the butterscotch ganache.