Grease a 9- by 13-inch baking pan and heat the oven to 350° F.
In the top of a double boiler, melt the chocolate and the butter together. Let cool.
Beat the eggs and the sugar well, then beat in the chocolate mixture and the vanilla extract. Add the sifted flour and nuts, if using, and stir until just combined. Pour into prepared pan and bake for 25 to 30 minutes (grandma says, "or more").
Meanwhile, quarter enough marshmallows to cover the top of the pan.
When the brownies are almost finished, make the frosting: Melt chocolate, marshmallows, and butter in the top of a double boiler. Add sugar and milk and beat until smooth (grandma says, "Beat until ready").
Remove baked brownies from the oven and immediately cover with the quartered marshmallows—no need to be dainty. Pour frosting over top and smooth with a nonstick spatula. Allow to cool completely before slicing into small pieces (I like to stick them in the freezer for an hour or so, and I then store them there, in a plastic container, too.)