Preheat oven to 375°F (190°C) and line baking sheets with parchment paper.
Cream the butter and both sugars in a large bowl until smooth.
Beat in eggs and vanilla until well combined.
Stir in flour, baking soda, and salt until just blended.
Mix in oats and butterscotch chips.
Drop by rounded tablespoons onto prepared baking sheets.
Bake for 8–10 minutes or until edges are golden brown.
Let cookies rest on the sheet for a few minutes before transferring to a cooling rack.