In the bowl of a stand mixer fitted with the paddle attachment, or in a large mixing bowl using a handheld mixer, beat the butter, brown sugar, and granulated sugar together until well combined (about 1-2 minutes). Add the egg and vanilla extract and mix until fully combined.
In a separate large mixing bowl, whisk together the flour, baking soda, ground cinnamon, and salt. Stir in the old-fashioned rolled oats.
Add dry ingredients to the wet ingredients and mix until just combined, then mix in the butterscotch chips until evenly distributed in the cookie dough.
Cover the cookie dough and refrigerate for at least 30 minutes.
Meanwhile, preheat oven to 350°F (177°C). Line two large baking sheets with parchment paper or silicone baking mats and set aside.
Once the cookie dough is chilled, remove it from the refrigerator. Using a 1.5 tablespoon cookie scoop, scoop the cookie dough and drop onto the prepared baking sheets, making sure to leave some space between each one. Roll into balls and slightly flatten each ball of dough.
Bake at 350°F (177°C) for 10-13 minutes or until the cookies are set and edges are lightly browned. Remove from the oven and cool on the baking sheets for 5-10 minutes, then carefully transfer the cookies to a wire rack to cool completely.
Notes
Store leftover cookies in an airtight container at room temperature for up to one week. Cookie dough may be prepared 2-3 days in advance, make sure to cover it tightly and store it in the refrigerator. If the cookie dough is too hard to scoop, let it sit at room temperature for 20-30 minutes.Freezing Instructions: Cookie dough will freeze well for up to 3 months, thaw overnight in the refrigerator. Baked cookies that have cooled completely will also freeze well for up to 3 months, thaw to room temperature before serving.Unsalted Butter: I recommend using unsalted butter since the amount of salt in salted butter can vary quite a bit between different brands. If you only have salted butter, just reduce the salt to a tiny pinch.Room Temperature Egg: If you forget to let your egg come to room temperature ahead of time, simply place it in a bowl of warm water for 5-10 minutes before using it.Oats: I highly suggest using old-fashioned rolled oats for these cookies to give them a chewier texture. You may also use quick oats, but keep in mind that the cookies won't be quite as chewy.