A little bagful of these will be a nice treat for your wedding guests.
Heat oil in an 8-quart pot over medium-high heat until hot but not smoking. Add popcorn kernels. Cover; cook, shaking occasionally, until kernels have popped; discard unpopped kernels. Transfer to a large bowl; sprinkle nuts over the top. Set aside.
Preheat oven to 250 degrees. Coat two rimmed baking sheets with cooking spray; set aside. Melt butter in a large saucepan. Add sugar, corn syrup, and salt. Cook, stirring, over medium heat until sugar is dissolved. Bring to a boil over medium-high heat, stirring constantly; boil until a candy thermometer registers 240 degrees.
Remove caramel from heat, and stir in baking soda and vanilla (mixture will bubble and steam). Immediately pour half the caramel over popcorn; stir until coated. Add remaining caramel, and stir until combined. Immediately spread on prepared baking sheets. Bake, stirring occasionally, until caramel coating is crisp and golden brown, about 1 hour. Scoop caramel corn into individual bags before serving.
Caramel corn can be stored in airtight containers at room temperature up to 3 days.