In a large bowl, beat the softened butter with both sugars until the mixture is light and airy.
Incorporate the eggs one at a time, ensuring each is fully blended before adding the next. Mix in the vanilla extract.
In another bowl, combine the oats, flour, baking powder, baking soda, salt, and cinnamon with a whisk. Slowly add this dry blend to the butter mixture, stirring until just combined.
Gently fold in the butterscotch chips. Wrap the dough and chill it for no less than 30 minutes.
Heat the oven to 350°F (175°C). Prepare baking sheets by lining them with silicone baking mats or parchment paper.
Using a medium cookie scoop, drop about 1 1/2 tablespoons of dough onto the sheets, spacing them 2 inches apart.
Bake for 9 to 11 minutes, until the edges turn golden. The centers might appear underdone, which ensures a chewy texture. Allow cookies to rest on the sheet for 5 minutes, then move them to a wire rack to cool fully.