Spread already popped popcorn out onto 2 large baking sheets. Remove any unpopped kernels. Set aside.
In a medium saucepan, melt butter over medium-high heat.
Add sugar, corn syrup, cream of tartar and salt. Stirring constantly, bring mixture to a boil for about 5 minutes.
Working quickly, remove the saucepan from the heat and stir in the baking soda. The mixture will become thick and bubbly.
Pour the caramel mixture over the popcorn and toss gently with a spatula or wooden spoon until all the kernels are coated.
Place baking sheets in the oven and bake for 30 minutes. Remove pans one at a time and stir each one again before heating for another 30 minutes.
Remove from oven. Let the popcorn cool on the pan. If desired, break apart any large clusters. Store in an airtight container for up to 2 weeks.
Notes
If making popcorn on the stove: In a medium saucepan, bring ¼ cup vegetable oil to a simmer over medium-low heat, stirring often. Add ½ cup popcorn kernels in a single layer and cover the saucepan with a lid. When the popcorn begins to pop (after about 2-3 minutes), shake the pot over the heat for about 3 minutes until popping slows. Remove from heat immediately and let cool.If making in the microwave: In a small mixing bowl, stir together ½ cup uncooked kernels and ¼ teaspoon vegetable oil. Pour into a brown paper bag and fold the bag closed. Microwave for approximately 2 minutes (will vary based on the microwave). Remove when popping has slowed. Remove from microwave and let cool before handling.