Start by lining a baking sheet with parchment paper. Melt sugar, butter, and water over medium heat, swirling occasionally until golden brown. Stir in Rice Krispies, baking soda, and salt, then spread thin to cool.
Cut butter into cubes and melt in a saucepan over medium heat. Let it bubble and foam until it turns golden and smells nutty. Pour over an ice cube, stir, and chill for 10 minutes.
Mix the cooled brown butter with brown and granulated sugar. Beat in the egg and vanilla until smooth. Fold in flour, baking soda, and salt until just combined.
Break the cooled brittle into small chunks. Gently fold half into the dough. Spread dollops of marshmallow fluff over the dough and scoop 1/4 cup portions onto a parchment-lined sheet.
Press extra brittle on top of each dough ball and bake at 350°F for 7–9 minutes. Cool for 5 minutes on the pan, then transfer to a rack. Use a cookie cutter to shape if desired.