Line a 9 x 13 baking dish or pan with parchment paper and preheat the oven to 350°F.
Cream the butter and sugar together in a large bowl with a stand or hand mixer until combined, about 2 minutes.
Add the vanilla and 1 egg and beat again. Separate the remaining two eggs—place the whites in a separate bowl and add the yolks to the bowl with the butter mixture. Mix again until evenly combined.
Add the flour, baking powder, and salt, and mix on low until no streaks remain.
Turn the dough out on the prepared baking sheet and press into an even layer with your fingers. You can also use a piece of parchment paper to keep your hands clean.
Top the dough with the chocolate chips and marshmallows.
Wash the beaters well and beat the egg whites on high until stiff peaks form, about 7 to 10 minutes. Fold in the brown sugar.
Spread the brown sugar meringue over the chocolate and marshmallows and smooth it out with a knife or offset spatula. Sprinkle the top with salt.
Bake for 30 minutes, until the meringue is golden brown. Let cool for a few minutes, then slice and serve.
