Add butter, sugar, and brown sugar to a bowl. Using a stand or hand mixer, mix the butter and sugars for 4-5 minutes until lighter and fluffy. Add eggs and vanilla and mix again.
Add flour, cornstarch, cinnamon, baking soda, baking powder, and salt. Mix until just barely combined. Add oats, toffee, white chocolate, and graham crackers. Mix until mix-ins are distributed throughout the dough.
If making small cookies, use a 1 tbsp cookie scoop to scoop out dough balls onto a lined baking sheet. Preheat the oven to 350 F and transfer the dough balls to the fridge while the oven preheats. When the oven is hot, bake for 8-11 minutes, until cookies are just starting to brown.
If making large cookies, measure out ½ cup of dough per cookie. Cover with plastic wrap and transfer to the freezer for 2 hours or the fridge overnight. Once it has chilled, preheat the oven to 350 F and bake the cookies on a lined baking sheet for 12-14 minutes, until edges are just starting to brown. Let the cookies cool completely.
