Preheat the oven to 350°F (175°C). Line a 9x13-inch baking pan with parchment paper, leaving an overhang for easy removal.
Make the crust: In a medium bowl, combine the flour, packed light brown sugar, baking powder, baking soda, egg, 1/2 cup melted unsalted butter, and vanilla until evenly mixed and combined.
Press the crust mixture firmly and evenly into the prepared pan.
Bake the crust for 12 minutes, then remove from the oven.
Immediately sprinkle the 4 cups miniature marshmallows evenly over the hot crust.
Return the pan to the oven and bake until the marshmallows puff and begin to turn golden, about 12 to 15 minutes. Watch closely to avoid overbrowning.
While marshmallows bake, make the topping: In a medium saucepan over medium heat, combine the peanut butter chips, 2/3 cup light corn syrup, and 1/2 cup unsalted butter. Stir constantly until melted and smooth, about 1–3 minutes.
Remove the pan from heat and stir in the salted peanuts (2 to 3 cups) and 2 cups Rice Krispies cereal until evenly coated.
Spread the warm topping over the puffed, golden marshmallows. Use a lightly greased spatula to press and flatten the topping into the marshmallow layer.
Let the bars cool completely in the pan. Once cool, lift them out using the parchment overhang and cut into bars. Sprinkle with flaky sea salt if desired.