Pop the popcorn using an air popper or other method. We use this hot air popper.
In a small saucepan, combine the oil, syrup, pumpkin puree, cinnamon, and salt. Cook over medium heat for a minute or two, whisking until all the ingredients are combined. Set aside to cool a bit.
Measure two cups of plain popcorn and set aside.
Put the remaining popcorn in a roasting pan. Gradually brush the pumpkin mixture on the popcorn, evenly spreading the mixture over the popped kernels. Alternately, you can slowly drizzle the pumpkin mixture onto the popped kernels. Be careful not to pour it on too quickly, or it will make the popcorn mushy.
Bake for 6 to 8 minutes, stirring every few minutes.
Let the popcorn mixture cool. The glazed pieces of popcorn will harden as they cool.
Stir the plain popcorn into the pumpkin-glazed popcorn mixture and serve.