Total time: 40 minutes
In a medium, heavy-bottomed saucepan, melt butter over medium heat. Add sugars, honey, and corn syrup and cook to 300° over medium-high heat, stirring occasionally. Mixture will be thick and bubbly. Add baking soda and stir carefully to incorporate.
Remove any unpopped kernels from popcorn, then place in a lightly oiled bowl. Pour caramel over popcorn and toss to combine, using oiled, heatproof spatulas or wooden spoons. When popcorn has cooled slightly but is not quite set, mix in salt and peanuts. With oiled hands, form into 2-inch balls. Keep a bowl of cold water nearby to dip your hands into if mixture gets warm or sticky. Place balls on sheet tray; once cool, store in an airtight container. Eat within a week.
For perfectly shaped kernels, use the mushroom variety of popcorn, available at JustPoppin.com