Preheat oven to 350 degrees F. Grease a 13 by 9-inch baking pan.
Melt the chocolate and butter in a 2-quart bowl in the microwave on high for 3 minutes, stirring every 20 to 30 seconds until the chocolate is completely melted. Add the eggs, sugar, and vanilla and mix well with a spatula. Add the flour and stir to combine. Spread the batter evenly in the prepared pan. Bake for 25 minutes.
While the brownies are baking, make the frosting. Melt the chocolate and butter in a medium bowl in the microwave on high for 3 minutes stirring every 20 to 30 seconds until the chocolate is completely melted. Add the egg substitute, vanilla, and sugar and stir with a spoon until smooth. Stir in the marshmallows; they will soften but not melt completely. Spread the frosting over the warm brownies. The frosting will set up when the brownies are completely cooled. When cool, cut into 1 1/2-inch squares and store in the refrigerator in a plastic container with a snap-on lid.