Preheat the oven to 350˚ F. Line a baking sheet with parchment paper. Beat the butter, granulated sugar and brown sugar in a large bowl with a mixer on medium-high speed until smooth and light, 1 to 2 minutes. Add the peanut butter and mix until smooth. Scrape down the bowl. Add the egg and vanilla and beat until smooth, about 1 minute.
Reduce the mixer speed to low. Add the flour, baking soda and salt and mix just until combined. Add the oats and mix just until combined.
Combine the dried cranberries, chocolate chips and peanuts in a small bowl. Add all but a few tablespoons of the cranberry mixture to the dough and mix just until combined. Refrigerate the dough until slightly firm, about 15 minutes.
Turn out the dough onto the baking sheet. Press into a 9-inch round, about 1/2 inch thick. Sprinkle the top with the reserved dried cranberry mixture and press to adhere. Bake until the cookie is crisp and golden around the edges and set in the center, 22 to 24 minutes. Transfer the pan to a rack and let the cookie cool completely on the pan. Cut into wedges.