Lightly grease a 9-by-13-inch baking dish with butter and line parchment paper, leaving a 2-inch overhang. Lightly grease the parchment.
Melt the butter in a large Dutch oven over medium heat until the foam begins to subside, about 4 minutes. Continue cooking, stirring constantly with a heat-resistant rubber spatula, until the butter solids brown in the bottom of the pan, another minute or two.
Add the marshmallows, cinnamon, salt and vanilla. Reduce the heat to low and cook, stirring, until the marshmallows are evenly melted. Remove the pan from the heat and stir in the puffed rice cereal until evenly coated.
Pour the mixture into the prepared baking dish and gently press down to smooth the top. Let cool to room temperature, about 20 minutes.
Cut into the desired shapes using a paring knife or cookie cutters.