Lightly butter a 9 x 13-inch baking dish and set aside.
Add the butter to a large pot. Melt over medium heat then continue to cook, stirring the butter often with a rubber spatula until the butter has browned and smells nutty.
Turn the heat down to low and add in the marshmallows. Stir to combine with the butter and continue to stir until the marshmallows have melted. Add the cinnamon and vanilla and stir to combine. Remove from heat.
Add the puffed rice cereal and apple chips; stir to coat them completely in the marshmallow mixture.
Transfer the mixture to the buttered baking dish, spreading in an even layer. Allow mixture to set before cutting into bars, at least 15 minutes. Store in a sealed container for up to 5 days.