Preheat oven to 300 degrees.
In a medium bowl combine flour, soda, and salt. Mix well with a whisk and set aside.
In the bowl of a stand mixer (or large bowl using a hand mixer), blend sugars at medium speed. Add butter and mix to form a grainy paste, scraping down the sides of the bowl. Add eggs, peanut butter, and vanilla, and mix until light and fluffy on medium speed.
Add the flour mixture and mix at low-speed until just mixed; do not overmix. Gently fold in the Reese’s Pieces with a wooden spoon until distributed evenly throughout the dough.
Drop large balls of dough onto an ungreased cookie sheets, the balls should be about the size of your palm. I fit 6 balls of dough onto each large baking sheet. Bake for 18-22 minutes until cookies are slightly brown on the edges. Transfer cookies to cookie racks to cool.