In a large saucepan, melt the butter over low heat. Once melted, add in the marshmallows and white chocolate chips. Stir until fully combined and melted.
Turn off heat.
Add Cheerios to marshmallow mixture and stir until fully coated and combined. Alternately, you could pour the marshmallow mixture on the Cheerios in a large bowl until fully combined and coated.
Using a buttered spatula/wooden spoon, press Cheerios mixture into a 9x13 parchment lined pan.
Add sprinkles, if desired, right on top of the Cheerios mixture.
Place in fridge and let cool for at least one hour.
Remove and cut into squares, enjoy!