In a small saucepan over medium heat, melt butter. Add garlic and cook 1 minute, stirring, then remove saucepan from heat and set aside to cool slightly.
Warm vegetable oil in a large, deep pot with a tight-fitting lid over high heat. When oil is hot, add unpopped popcorn, cover pot, and cook 1 minute. Vigorously slide pot back and forth over burner until popcorn begins to pop. Continue cooking and shaking pot until popping subsides, about 5 minutes. Remove pot from heat and transfer popcorn to large serving bowl.
Pour butter-garlic mixture over popcorn, sprinkle with Parmesan and cayenne and toss to coat. Season with salt and serve.