Preheat the oven. Preheat your oven to 350°F and position the oven rack in the center. Then, line two cookie sheets with parchment paper or lightly coat them with cooking spray.
Cream the butter and sugar. In a large mixing bowl, beat the softened butter, granulated sugar, and brown sugar together using an electric mixer on medium speed until the mixture is light and fluffy. This should take about 3-5 minutes.
Add the wet ingredients. Add the egg and vanilla extract to the creamed butter and sugar mixture. Mix until fully combined, scraping down the bowl's sides as needed to make sure everything is evenly incorporated.
Mix the dry ingredients. Whisk together the flour, baking soda, and salt in a separate bowl. Then, slowly add to the wet ingredients, mixing at low speed. Mix it in batches until it's combined after each addition. Be careful not to overmix.
Fold in the butterscotch chips. Once the dough is well mixed, use a spatula to fold in the butterscotch chips, making sure they are evenly distributed.
Scoop the dough. Scoop approximately 1 tablespoon of cookie dough for each cookie and place the scoops onto the prepared cookie sheets, spacing them about 2 inches apart. Each sheet should fit around 15 cookies.
Bake. Bake in the preheated oven for 10-12 minutes or until the edges of the cookies are golden brown. The centers should still be soft. Remove the cookies from the oven and allow them to cool on the cookie sheets for 5 minutes before transferring them to wire racks to cool completely.