Line two baking sheets with parchment paper and set aside then start with the dry ingredients. Whisk both flours, baking soda, and salt together and set aside.
Using a mixing bowl and hand mixer or a stand mixer fitted with the paddle attachment, cream together butter and both sugars. Add eggs, one at a time and vanilla extracts, and mix between each addition, scraping down the sides of the mixer bowl as needed.
Add the dry ingredients to the wet ingredients in a few batches (or just one if using a large stand mixer). Remove the bowl from stand mixer or set aside hand mixer and stir butterscotch chips in by hand using a wooden spoon or sturdy spatula.
Slightly overfill a large, 2-oz cookie scoop to place up to 8 cookies on each parchment-lined cookie sheet.
Chill dough on trays for 45 minutes in the fridge (60 minutes if you used room temperature butter in the cookie dough). When there is about 15 minutes left of chill time, preheat the oven to 350 degrees.
Bake for 20 minutes, rotating each baking sheet and swapping oven racks halfway through the baking time. Cookies are finished baking when the bottom edges of the cookies start to turn golden brown.
Transfer each cookie sheet to a wire rack and let the cookies cool completely on the trays.