Preheat the oven to 350 degrees.
Prepare a 9 x 9 inch baking pan by lining it with parchment paper leaving an overhang on two sides.
Combine flour, brown sugar, baking powder, baking soda, and salt in a medium bowl.
Add softened butter to the mixture and use your hands to mix in into the flour mixture.
Add egg yolk and vanilla and mix until evenly combined. The mixture will be very crumbly.
Press into a 9 x 9 pan using a cup to press it tightly into the pan.
Bake for about 12-13 minutes until golden brown.
Remove the crust from the oven and immediately add the marshmallows to the crust, distributing them evenly.
Return to the oven for 2 minutes until the marshmallows start to puff up. Remove from the oven and set aside while you make the topping.