Preheat oven to 350 degrees F and grease cookie sheets.
Cream together the butter, sugar, and brown sugar. Let the mixer beat the mixture for 3-4 minutes to get a fluffy and light mixture.
Add in the eggs, vanilla extract, vanilla pudding mix, salt, and baking soda. Scrape down the sides of the bowl a couple of times to make sure that everything is fully incorporated.
Slowly mix in the flour until the dough starts to pull away from the sides of the bowl.
Either using the mixer or a spoon, stir in the Reese's baking cups and pieces mixture. I used the mixer so it could break up the pieces a little.
Using an ice cream scoop or spoon, form the dough into balls and place on the greased cookie sheet.
Bake the cookies for 9-11 minutes, just until you see the edges slowly start to turn golden brown.
Allow the cookies to cool for a few minutes on the baking sheet, then transfer to a wire cooling rack if you are storing. If not, eat warm and enjoy!
