Cover baking sheet with parchment paper if desired and set aside.
Add softened butter, brown sugar, and white sugar to stand mixer bowl (or large mixing bowl). Using stand mixer (or hand mixer), mix ingredients together on low speed 30 seconds, then increase speed to medium. Continue mixing 2 to 5 minutes, until ingredients are creamed. Mixture should be fully combined, light, and fluffy. Note: Be careful not to overmix. Overmixing will make mixture greasy and soupy. If you overmix, discard mixture and start again.
Once butter and sugar are creamed, pause mixer and crack egg directly into mixing bowl. Add vanilla extract, then resume mixing on low speed. Mix until ingredients are just combined.
Sift flour through sifter and directly into mixing bowl, making sure any clumps of flour are broken up. Once all flour has been sifted, add baking soda and salt to mixing bowl. Resume mixer and mix until ingredients are just combined.
Once dough has formed, add butterscotch chips to mixing bowl. Use silicone spatula to gently fold chips into dough mixture until chips are just incorporated. Be careful not to overmix.
Use cookie scoop to portion dough into equal-sized scoops. Each scoop should be 1 tablespoon of dough for smaller cookies, up to 3 tablespoons of dough for larger cookies. Place dough ball on baking sheet and repeat with remaining dough. Make sure to place dough balls on baking sheet approximately 1 to 2 inches apart.
Place baking sheet filled with cookie dough balls in refrigerator. Chill dough at least 2 hours and no more than 36 hours. If chilling dough more than 2 hours, cover baking sheet with plastic wrap before refrigerating.