Preheat the oven to 375°F and line baking sheets with parchment paper.
In a large bowl, cream together the butter, sugar, brown sugar, and pudding mix on medium speed for 2 minutes, until light and fluffy.
Beat in the vanilla, eggs, and peanut butter until fully incorporated.
Add baking soda, salt, and flour. Mix just until combined. Do not overmix.
Gently fold in chocolate and butterscotch chips.
Scoop dough into 3-tablespoon balls and refrigerate for 30 minutes to prevent spreading and create a thicker cookie.
Bake for 10–12 minutes, until edges are lightly golden and centers look slightly underbaked.
Allow cookies to cool on the pan for 5 minutes before transferring to a rack.