Put the vegetable oil and a few test popcorn kernels in a large pot. Heat over medium-high heat until the kernels pop, then carefully add the remaining kernels in a single layer. Cover and cook, shaking the pot, until there are several seconds between pops. Transfer the popcorn to a bowl. Lightly oil a baking sheet.
Wipe out the pot, then add the sugar, corn syrup, molasses, peanut oil, 1/4 teaspoon salt and the peanuts. Cook over medium-high heat, stirring often, until a candy thermometer registers 290 degrees F, about 8 minutes. Remove from the heat and stir in the popcorn until coated. Transfer the caramel corn to the prepared baking sheet and let cool, then break into small pieces.
Special "mushroom" kernels pop into these round shapes found in Cracker Jack.