Line a 9 x 13-inch metal pan with parchment, leaving enough overhang on two sides to lift out the slab. Rub the parchment and exposed ends of the pan with the reserved 5 g softened butter. Weigh 510 g marshmallows into one bowl and the remaining 57 g into another, then measure the cereal separately. Having everything ready matters because the mixture begins thickening as soon as the cereal is added.
Place the remaining 165 g butter in a heavy-bottomed 5 to 6-quart saucepan. Melt over medium heat, stirring and scraping the bottom with a heat-resistant spatula. The butter will foam, crackle, and then quiet as its water evaporates. Continue cooking for 6 to 8 minutes, until the milk solids beneath the foam are chestnut brown and smell nutty. Remove the pan from the heat immediately if the specks begin turning very dark, since they can burn quickly.
Reduce the burner to low and return the saucepan to the heat. Add the 510 g portion of marshmallows and stir continuously, scraping the browned milk solids from the bottom so they disperse through the mixture. Cook for 2 to 4 minutes, just until no large marshmallow lumps remain and the mixture looks glossy and elastic. Do not let it boil. Remove from the heat, then stir in the vanilla and fine salt until evenly incorporated.
Immediately add the crisp rice cereal to the saucepan and fold with the silicone spatula, bringing the mixture up from the bottom rather than stirring aggressively. When the cereal is almost evenly coated but a few dry patches remain, fold in the reserved 57 g marshmallows. Transfer to the prepared pan while warm. Use the buttered spatula to spread the mixture into the corners and level the top with light, broad presses. Stop once the layer is even because firm packing will make the bars hard.
Leave the pan uncovered at room temperature for about 60 minutes, until the slab feels set at the edges and no longer shifts when the pan is nudged. Do not refrigerate it to speed cooling because cold air can make the bars firm and encourage surface moisture later. Lift the slab out using the parchment and place it on a cutting board. With a large sharp knife, cut into 24 bars, wiping the blade if sticky marshmallow begins pulling at the edges.