In the bowl of a stand mixer fitted with the paddle attachment (or large bowl and electric hand mixer), cream together the first 5 ingredients (through vanilla) on medium-high speed until light and fluffy, about 5 minutes.

Stop, scrape down the sides of the bowl, and add the flour, baking soda, salt, and mix on low speed until just incorporated, about 1 minute; no longer.

Add the Reese's Pieces, chocolate chips, and blend until just incorporated.

Scoop out cookie dough into 2-inch balls. Place mounds on a large plate, flatten mounds slightly with your palm, cover with plastic wrap, and refrigerate for at least 2 hours, or up to 5 days, before baking. (Tip: If you need to save time, place cookie dough on baking sheet (lined with parchment or silpat and freeze for 15 minutes.)

Preheat oven to 350F, line a baking sheet with a siplat, parchment paper or spray with cooking spray. Place mounds on baking sheet, spaced at least 2 inches apart. Bake for 8 to 9 minutes, or until edges have set and tops are just beginning to set, even if slightly undercooked, pale and glossy in the center. Do not bake longer than 10 minutes because cookies will firm up as they cool Allow cookies to cool on the baking sheet for 5 minutes before removing and transferring to a rack to finish cooling.

Cookies will keep airtight at room temperature for up to 1 week, or in the freezer for up to 4 months. Alternatively, unbaked cookie dough can be stored airtight in the refrigerator for up to 5 days.