Line a baking sheet with parchment or wax paper. Warm oil in a large pot over high heat. Add popcorn, cover and cook, shaking pot, until all corn is popped. Transfer to a large bowl, add peanuts and set aside.
In another large pot, combine 1/4 cup water, sugar and corn syrup. Bring to a boil over medium-high heat. Reduce heat to medium and cook without stirring until mixture turns a light amber color, 4 to 6 minutes longer. If parts of syrup are turning darker than others, gently tilt pot to even out heat.
Remove pot from heat and stir in butter, vanilla and salt. Stir caramel into popcorn and peanuts to completely coat. Scrape mixture onto prepared baking sheet and let cool, about 15 minutes, before breaking into pieces and serving.