Preheat oven to 350°F. Line 13x9-inch baking pan with heavy foil, extending the foil over the edges of the pan to allow for easy unmolding after baking.
In a small bowl, whisk together flour, baking power, baking soda, and salt. Set aside.
In a large bowl, beat butter using an electric hand mixer or stand mixer fitted with paddle attachment until smooth. Add brown sugar, yolks, and vanilla. Mix until well combined. Scrape down sides of bowl as needed.
Add in flour mixture. Mix on low speed until incorporated. Press dough mixture into the bottom of prepared baking pan.
Bake for 10-12 minutes until crust is lightly browned. Immediately sprinkle mini marshmallows over crust in even layer. Return to oven for 2-3 minutes until marshmallows have softened. Use a greased mini offset spatula to spread warm marshmallows to an even layer.