Preheat oven to 175 degrees and grease a 9x13 inch brownie tin (two loaf tins will suffice if you don't have one of these - just split the mixture between them).
Melt white chocolate and butter together in a bowl over a pan of simmering water, making sure the water doesn't touch the bottom of the bowl. Set aside to cool.
In a second bowl, sift flour and baking powder. In a third bowl, mix together eggs, brown sugar and vanilla, then add the melted butter/chocolate mixture, stirring well. Fold flour mixture into egg mixture until smooth. Finally, add the chocolate chunks/chips and mini marshmallows. Pour evenly into prepared tin/s.
Bake for 15-20 mins, until top is crispy and just firm to the touch. Cool in tin then cut into squares.