Place oil and 2-3 kernels in a large pot, cover, and heat over medium heat. When kernels pop, add remaining kernels in a single layer, sprinkle with a little salt, cover, shake well, and continue to heat over medium heat. When popping slows down to a few seconds between pops, remove from heat.
Place brown sugar and butter in a microwave-safe bowl and microwave for 2 minutes. Add corn syrup and marshmallows and microwave until they are melted, about 1 ½ to 2 minutes. Stir and immediately pour over popcorn and stir to distribute.