Preheat the oven to 350°F.
Combine the flour, baking powder, and baking soda in a medium-size mixing bowl.
Cream the cooled melted butter and sugars together in a large mixing bowl with an electric mixer on medium speed until smooth. Add the eggs and vanilla extract and beat until smooth. Beat in the flour mixture until just combined. Stir in the oats and peanuts. Stir in the Reese's Pieces. Place the bowl in the refrigerator for 10 minutes (or up to 6 hours) to let the dough firm up.
Drop the batter by heaping tablespoonfuls onto ungreased baking sheets, leaving about 3 inches between each cookie. (Balls of dough may be placed next to each other on parchment paper-lined baking sheets, frozen, transferred to zipper-lock plastic freezer bags, and stored in the freezer for up to 1 month. Frozen cookies may be placed in the oven directly from the freezer and baked as directed.)
Bake the cookies until they are golden around the edges but still soft on top, 15 to 17 minutes (a minute or two longer for frozen dough). Let them stand on the baking sheet for 5 minutes, then remove them with a metal spatula to a wire rack to cool completely. Reese's Pieces Autumn Oatmeal Cookies will keep at room temperature in an airtight container for 2 to 3 days.
