Preheat your oven to 325°F and line baking sheets with parchment paper.
In a generous mixing bowl, blend the softened butter until it achieves a creamy consistency.
Add the granulated sugar and the brown sugar to the bowl, then beat until the mixture attains a smooth and cohesive texture.
Incorporate the room-temperature egg, milk, and pure vanilla extract, ensuring a thorough but gentle blending. Avoid over-mixing to preserve the cookie's texture.
In a separate bowl, combine the all-purpose flour, baking soda, salt, and ground cinnamon.
Gradually introduce the dry ingredients into the wet mixture, stirring well until a harmonious dough forms.
Add the old-fashioned rolled oats incrementally, ensuring they become well integrated into the dough.
Finally, gently fold in the butterscotch chips, reserving a portion for later use.
Using an ice cream scoop or approximately 2 tablespoons of dough, place portions of cookie dough onto the prepared cookie sheets, leaving about 2 inches of space between each cookie. Sprinkle the reserved butterscotch chips on top of each cookie.
Bake in the preheated oven for 10-12 minutes, or until the edges turn golden brown while the center remains slightly soft.
Remove the cookies from the oven and allow them to cool on the baking sheets for 10 minutes. Afterward, transfer them to a wire cooling rack to cool completely.
Store the Butterscotch Oatmeal Cookies in an airtight container to keep them fresh and delicious. Enjoy!