Heat oil in a Dutch oven over medium-high heat. Add kernels; cover and cook 4 minutes, shaking pan frequently. When popping slows, remove pan from heat. Let stand.
Melt butter in a pan over low heat. Add marshmallows; cook 2 minutes. Remove from heat. Add 3 cups popcorn and remaining ingredients; stir. Cool 2 minutes. Form into 10 (3-inch) balls. Cool 5 minutes.
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