1. Preheat oven to 325°. Put popcorn in a large roasting pan. Line a large baking sheet with waxed paper.
2. In a medium saucepan over medium heat, use a heatproof spatula or wooden spoon to stir together 1 1/4 cups butter, the honey, and salt until butter is melted. Increase heat and boil honey mixture gently 1 minute, stirring constantly. Stir in vanilla.
3. Carefully pour honey mixture over popcorn in roasting pan and stir gently to coat. Bake popcorn, stirring every 5 minutes, until deep golden all over, about 25 minutes.
4. Let popcorn stand 5 minutes, or just until cool enough to handle. Working quickly with lightly buttered hands, press small handfuls of the mixture into 1 1/2-in. balls, occasionally loosening popcorn from bottom of pan with a spatula. If mixture cools too much to be malleable, return it to oven for about 45 seconds to soften.
5. Put popcorn balls on prepared baking sheet and let cool completely. Store in an airtight container at room temperature for up to 2 weeks.
Note: Nutritional analysis is per popcorn ball.
If you don't have an air popper, you can pop the popcorn in the microwave: Working in 2 batches, put kernels in a brown paper bag (any size). Do not add oil. Fold the bag's opening several times to seal, then microwave at full power in 1-minute increments, checking popcorn and removing popped kernels as you go (they burn easily). Be careful when opening bag; it will release steam.