Preheat the oven to 250 degrees and line 2 half sheet pans with parchment paper.
Pop the kernels in two batches, ¼ cup at a time, in brown paper bags, in the microwave using the popcorn setting.
Transfer the fully popped kernels to a very large bowl sprayed with non-stick cooking spray, and discard the partially popped and unpopped kernels.
In a medium-sized saucepan, melt the butter over high heat.
Add the sugar and syrup and stir to combine.
Bring to a boil and cook, without stirring, to 238-degrees (soft ball stage) on a candy thermometer.
Remove from the heat and stir in the vanilla and salt.
Carefully pour the hot sugar mixture over the popcorn and toss, using two rubber spatulas, until the popcorn is evenly coated.
Divide the popcorn onto the two prepared sheet pans and, using a rubber spatula, separate the popcorn as best you can.
Bake for 20 minutes, then toss with a flat spatula.
Bake for an additional 15 minutes, then cool completely on the sheet pans.
Store in an airtight container for up to 5 days.