Heat oil with 3 kernels in a 3-quart heavy saucepan, covered, over moderate heat until 1 or 2 kernels pop. Remove lid and quickly add remaining kernels, then cook, covered, shaking pan frequently, until kernels stop popping (or until your shoulder gives out), about 3 minutes. Remove from heat and uncover.
I ended up with 6 cups of popped popcorn.
(Premium American-brands of popcorn will yield more than mine did, about 8 cups of popcorn. If so, you may need to prepare 2 baking sheets in the next step.)
Line bottom of a large shallow baking pan with foil and lightly oil foil, or use a non-stick baking sheet.
Melt butter in a 6-quart heavy pot or Dutch oven over moderate heat. Add brown sugar and corn syrup, and salt and bring to a boil over moderate heat, stirring, then boil, without stirring, until syrup registers 300 degrees F on thermometer, 8 to 10 minutes. Remove pot from heat.
Using a wooden spoon or a heatproof spatula, stir vanilla and baking soda into the syrup, then quickly stir in peanuts and popcorn to coat. Immediately spread mixture over baking pan as thinly and evenly as possible.
Let cool completely, then break into bits.