In a medium bowl, whisk the flour, baking soda, and salt until combined. Set aside.

In the bowl of an electric stand mixer fitted with a paddle attachment, cream the butter until smooth. Add in both sugars and mix on high for 3 minutes until light and fluffy. Add the eggs one at a time, mixing after each addition until combined. Add in the vanilla. Then stir in the pudding mix.

With mixer set on low speed, slowly add the flour mixture into the wet mixture until everything has been incorporated. Remove bowl from the mixer, and stir in chopped Reese's cups and Reese's pieces by hand.

Cover bowl with plastic wrap and chill in the refrigerator for at least 2 hours, or up to 3 days.

Using a 1/4 cup measuring cup or two spoons, scoop balls of chilled cookie dough onto lined baking sheet, placing them about 2 inches apart. Lightly press the top of each cookie, but don't smash them down--this will allow them to bake more evenly so you don't end up with a lump in the center. Press a few more Reese's pieces or chopped peanut butter cups on top of each cookie dough ball, if desired.

Bake cookies for 10 -12 minutes*, or until slightly browned around edges. The centers might look underdone at first, but they will finish baking up as they cool. Allow cookies to cool on baking sheets for 5 minutes before transferring to a wire rack to cool completely.

Cookies will stay fresh in an airtight container at room temperature for up to 1 week, or in the freezer for up to 6 months.