Preheat the oven to 350°F. Spray a large roasting pan with nonstick cooking spray.
Place the Bugles, Chex, pretzels, and peanuts in the prepared pan. Mix and set aside.
In a heavy 2-quart saucepan, combine the brown sugar, butter, corn syrup, and salt. Cook over medium heat, stirring occasionally, until the mixture comes to a full boil. Remove from the heat, add the vanilla and baking soda, and stir. The mixture will foam up and expand.
Pour the syrup over the cereal mixture and toss to coat.
Bake the Chex mix on the center rack for 15 minutes, removing every 5 minutes to stir.
Remove the Chex mix from the oven and spread it out over wax paper to cool for about 2 minutes before sprinkling the Reese’s Pieces on top.
When completely cool, store in an airtight container.