Preheat oven to 350F. Spray or line with parchment paper two baking sheets. In a medium bowl, whisk together flour, baking soda, baking powder and salt; set aside.

Using an electric mixer on medium speed, beat butter until smooth and creamy. Add peanut butter and beat until completely combined. Add both sugars and beat on medium-high until light and fluffy, 3-4 minutes. Scrape sides of bowl, add egg and vanilla, and beat until completely incorporated. Scrape down sides and bottom of bowl, add flour mixture all at once, and beat until just incorporated, about 30 seconds. Using a rubber spatula, stir in the butterscotch chips.

Scoop 2 Tbsp of dough into balls and place on prepared baking sheets at least 1½ inches apart. Bake for 5 minutes until cookies just start to brown on edges, another 5-6 minutes. Remove from oven and place pans on cooling racks for 5 minutes. Transfer cookies from pans to wire racks and cool completely. Cookies can be stored in an airtight container at room temperature for up to 5 days.