In a 3-quart saucepan, heat 3 tablespoons (36 grams) oil over medium-high heat. Add 3 kernels; cover pan tightly with lid. When kernels have popped, add half of remaining kernels in an even layer. Cover pan tightly with lid, and reduce heat to low; cook until rapid popping has almost completely stopped, about 30 seconds. Transfer to a large bowl. Repeat with remaining oil and remaining kernels. (You should have a total of 16 cups [180 grams] popcorn.)

Preheat oven to 200° (93°C).

Divide popcorn between 2 large rimmed baking sheets. Sprinkle ⅓ cup (47 grams) peanuts on popcorn on each pan. Spread mixture to an even layer.

In a large saucepan, combine brown sugar, butter, corn syrup, and salt. Cook over medium heat, stirring occasionally, until mixture begins to bubble around edges. Cook for 5 minutes. Remove from heat. Stir in baking soda. (Mixture will foam.) Pour brown sugar mixture over popcorn mixture. Gently stir to coat evenly.

Bake for about 1 hour, stirring every 15 minutes. Let cool completely on pans on wire racks. Store in airtight containers.