Make the crispy Special K coating: Melt the remaining 4 tablespoons butter in a large bowl. Add 3 cups Special K. Toss to combine. Add the remaining 3 tablespoons sugar and season with ¼ teaspoon salt. Mix and set aside.
Make the cookie dough: Let 1 stick butter sit on the counter until room temperature, or soften in the microwave in spurts of 5 seconds until a finger leaves an indentation. Combine the softened butter, ½ cup brown sugar, and ¼ cup granulated sugar in the bowl of a stand mixer fitted with the paddle attachment. Cream on medium-high speed, scraping down the bowl once or twice, until lightened and fluffy, about 3 minutes. Add 1 egg, ½ cup peanut butter, 2 tablespoons vanilla extract, 2 tablespoons water, and 1 ½ teaspoons salt. Mix on medium, again scraping down the bowl, until combined, 1 minute. Add ¾ cup flour and 1 teaspoon baking powder directly on top of the flour. Use a fork to disperse the baking powder into the flour. Beat on medium-low just until no dry bits remain.
Form and CHILL!: Working one at a time, scoop ten 2-ounce(ish) portions (about ¼ cup each) of dough and drop it right into the Special K topping. Use your fingers to coat the dough with the topping, pressing it to adhere, gently forming the dough into a ball shape as you do. It is a very soft and sticky dough. That’s okay! The Special K coating will act as a barrier between your hands and the dough to help you form them. Repeat until all 10 cookie dough balls have been formed. Transfer them to a small plate or small baking sheet. Tear 5 JUMBO-sized marshmallows in half. Place one half (torn side face up) on top of each dough ball. Using your middle finger, press the marshmallow deep down in the dough ball, like you would a thumbprint cookie. You can re-shape the surrounding dough a bit to make nice tidy little nests. Freeze until firm, about 45 minutes to 1 hour. If you are using regular marshmallows, place 1 ½ in each nest.
Bake: Preheat oven to 350. Once chilled and ready to bake, divide the cookies among 2 parchment lined baking sheets–you can fit 5 on each. Melt 1 tablespoon butter however is easiest for you. Brush the tops of each marshmallow lightly with butter. Bake until the edges are deeply golden and marshmallows have melted and caramelized, about 18-22 minutes. Repeat with remaining unbaked mounds of dough.
