Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x13-inch pan.

Combine butterscotch chips and butter in a microwave-safe bowl; microwave on high for 1 1/2 minutes. Stir, then continue to cook in 15-second intervals, stirring after each interval, until melted and smooth, 1 to 3 more minutes. Set aside to cool slightly.

Stir brown sugar, eggs, and vanilla together in a large bowl. Mix in melted butterscotch chips, then mix in flour, baking powder, and salt until smooth. Stir in marshmallows and chocolate chips. Spread batter evenly into the prepared baking pan.

Bake in the preheated oven until the top is dry and the edges have started to pull away from the sides of the pan, 15 to 20 minutes. Cool completely, then cut into 24 squares.