Place the popped popcorn in an extra large bowl, with plenty of room to stir. Melt the butter in a large saucepan over medium high heat. Add the marshmallows, and stir constantly until smooth. Pour the marshmallow mixture over the popcorn, and use a wooden spoon to completely cover the popcorn.
Let the mixture sit for about 5-10 minutes, to let the marshmallow cool--but not harden. Coat your hands with butter, then form the popcorn mixture into balls. Place them on a piece of wax paper that has also been rubbed with a little butter. Don't use cooking spray--it leaves a yucky taste on the popcorn.
Once all the popcorn balls are formed, push the popsicle/sucker sticks into the center of each ball. Melt the white chocolate chips in a glass bowl in the microwave. Start with 30 seconds, stir, then another 15-30 seconds and stir until smooth. Dip the top half of the popcorn balls into the white chocolate, then immediately add the sprinkles. Refrigerate until time to serve. Makes 6-8 popcorn balls, depending on size.