Heat oven and prepare pan. Preheat oven to 350 degrees F. Line a baking sheet with parchment paper.
Mix the dough. Whisk melted butter together with brown sugar and peanut butter until smooth. Add eggs and vanilla extract. Mix until eggs are combined and the mixture is smooth. Switch to a rubber spatula or wooden spoon. Add the gluten-free flour, baking soda, and salt. Mix until flour is combined. Add the oats, butterscotch chips, peanuts, and candy pieces.
Drop dough onto pan. Scoop dough, about two tablespoons each, onto prepared baking sheet. Space cookies about one-inch apart. If desired, flatten each cookie with the bottom of a glass or measuring cup. Dip the bottom of the measuring cup in cold water to keep it from sticking to the dough.
Bake until set. Bake until edges are golden brown and set, about 12 minutes. Allow cookies to cool on the pan for about three minutes and then transfer cookies to a wire rack. Repeat with remaining dough.
Cool on a rack. Allow cookies to cool on the pan for about three minutes and then transfer to a wire rack to cool completely.
Store in an airtight container or freeze. Place cookies in an airtight container and store on the counter for up to four days or freeze in a freezer container, for up to three months. Allow cookies to thaw on the counter.
Gluten-Free Flour: This recipe was tested with Bob's Red Mill 1:1 Gluten-Free Flour Blend and is recommended for the best texture.
Oats: Use gluten-free oats. Quick cook (instant) oats or old fashioned oats may be used. Do not use steel cut oats in this recipe.