Pour the sugar into the center of a deep saucepan fitted with a candy thermometer. Carefully pour the water around the walls of the pan, trying not to splash any sugar onto the walls. Do not stir; gently draw your finger twice through the center of the sugar, making a cross, to moisten it.
Over high heat, bring to a full boil and cook without stirring until golden caramel, about 10 to 15 minutes and the temperature reaches 320 to 330 degrees F. Swirl the mixture occasionally to even out the color. Turn off the heat and stir in the butter then the popcorn, peanuts, and cherries.
Pour onto a silpat or buttered sheet pan and let cool a few minutes then start breaking it up into clusters, working quickly, so it doesn't harden and you don't burn yourself. Store in an airtight container for up to 1 week.
Notes: I use Black Diamond Popcorn with its petit size "hulless" kernel. To pop corn properly, place the kernels in a heavy-bottomed large pot and cover them with oil. Put the lid on and cook on high until you hear the first pop. Immediately take it off the heat and let it sit 1 minute. Then return it to the heat and finish popping, shaking the pan the whole time. I don't know why this is better, but this is what my dad does, and his popcorn was always the best.