Toast the marshmallows on all sides using your preferred method (fire pit, over a stovetop burner, with a kitchen torch, or – with an extremely watchful eye – the broiler.) Transfer to a parchment lined baking sheet and chill at least two hours in the refrigerator.
Preheat the oven to 375° F. Line an 8 x 8-inch baking pan with parchment paper, leaving an overhang at two edges to help lift the bars from the pan. In a small bowl, combine the flour, baking powder, and salt. Stir to blend. In the bowl of an electric mixer, combine the butter, sugars, and seeds scraped from the vanilla bean. Beat on medium-high speed until light and fluffy, 2 minutes. Blend in the egg and vanilla. With the mixer on low speed, blend in the dry ingredients just until incorporated. Remove the marshmallows from the refrigerator, coarsely chop (as best you can with something so sticky), and add to the mixing bowl. Blend into the cookie dough just until no large globs remain. Transfer the dough to the prepared baking pan and press down into an even layer.
Bake until lightly browned on top and just set in the center, about 25-30 minutes. Remove from the oven and transfer to a wire rack to cool at least 30 minutes. Use the parchment paper to lift the bars from the pan. Transfer to a cutting board and slice into 16-20 bars.