Add 1 tablespoon of the oil to a 4 quart saucepan, and heat over high heat. When oil is hot, add 1/2 cup of popping corn. Keep pan moving constantly. When corn stops popping, remove from heat. Place popped corn in oven to keep warm. Repeat until all corn has been popped. Set aside.
In a medium saucepan with a candy thermometer inserted, combine butter, sugar, and corn syrup. Stir well and bring to boiling over medium heat. Stir in condensed milk; simmer, stirring constantly, until thermometer reads 238 degrees F (114 degrees C). Stir in vanilla.
Pour caramel over popped corn and stir to coat. Butter hands lightly; shape popcorn into balls about 3 1/2 inches in diameter.