Preheat oven to 350°F and line two large baking sheets with parchment paper. If you don't have parchment paper, you can just drop the cookies onto an ungreased sheet pan, they won't stick.
In a medium bowl, whisk together the flour, baking powder and pudding mix. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream together butter, cream cheese, and sugar until light and fluffy, about 1 minute. Scrape bowl with silicone spatula.
Add the egg and vanilla and mix until combined. Scrape bowl with silicone spatula.
On low, add half of the dry ingredients and mix until mostly combined. Add the remaining dry ingredients and mix on low until just combined. The dough should be difficult to mix.
Use a cookie scoop to drop balls of dough onto the sheet pans 1" apart. Press a few butterscotch chips into the top of the cookie dough balls, and press down to flatten the cookies slightly. If you'd like a uniform edge on your cookies, roll the dough balls briefly in your hand before pressing the chips into them. The cookies will not spread much in the oven, it's important to pat them down a bit.
Bake for 12 to 14 minutes, or until the edges of the cookies look dry and are starting to brown. Let them cool on the sheet pan for 3 minutes before transferring to a cooling rack to cool completely.