Position an oven rack in the center of the oven, and preheat to 350 degrees F. Line a 9-by-13-inch baking pan with aluminum foil, leaving about a 2-inch overhang on all sides; butter the bottom and sides.
Pulse 2 cups of the pretzels in a food processor to a fine powder; transfer to a medium bowl, add the flour, baking powder and salt, and stir to combine.
Melt the butter in a medium saucepan over medium heat. Remove from the heat, and stir in the sugar; set aside to cool completely. Stir in the eggs and vanilla until completely combined. Add the pretzel-flour mixture in 2 batches, stirring after each until fully incorporated. Stir in the butterscotch chips and half the chocolate chips.
Transfer the dough to the prepared pan, and spread it out evenly. Push the potato chips and the remaining 1/2 cup pretzel sticks into the top of the batter. Scatter the remaining chocolate chips. Bake until golden and a toothpick inserted in the center comes out with only a few crumbs attached, 30 to 35 minutes. Cool completely in the pan on a rack. Use the foil overhang to help lift the bars out of the pan. Cut into 24 squares. Store at room temperature in an airtight container for up to 3 days.
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