Line a 9 x 9 inch baking pan with foil. Use 1 tablespoon softened butter to butter the bottom and sides. Set aside. Roughly chop the fudge grahams.
On the stove top in a heavy bottomed saucepan, melt together the chocolate chips, sweetened condensed milk, 2 tablespoon butter and salt.
Cook over medium, stirring until completely smooth. Remove from the heat and add the vanilla. Mix well.
Mix in ½ of the chopped fudge grahams and 2 cups of mini marshmallows. Stir until evenly distributed, then pour into the pan.
Spread evenly then top with the remaining chopped fudge grahams and mini marshmallows. Press gently into the top of the warm fudge.
Brown the marshmallows under the broiler or using a pastry torch, if desired.
Chill for at least 4 hours before cutting.
Lift from the pan using the foil. Peel back to cut into equal pieces. Store chilled.