In a small saucepan, combine 1 cup water, 1/2 cup of the sugar, the chocolate and the vanilla. Heat over medium heat, stirring constantly, until melted. Set aside to cool.
Preheat the oven to 350 degrees F.
Prepare three 9-inch round cake pans: spray the bottom and sides of each pan with cooking spray; line the pans with parchment paper; then spray again with cooking spray.
Sift together the flour, baking powder and salt. In a stand mixer, cream the butter and the remaining 1 3/4 cups sugar until smooth. Add the eggs, one at a time, beating after each addition. Add the cooled chocolate mixture and beat until smooth. Add the sifted flour mixture alternately with the milk, starting with a third of the flour, then adding half the milk, and ending with the flour. Stir only enough after each addition to blend the ingredients. Pour the batter evenly into the cake pans and bake for 35 minutes, or until done. Judge doneness by appearancelayers will begin to pull away from the sidesor by inserting a toothpick into the center of a layer. The toothpick should come out clean. Cool the cakes in the pans for 10 minutes, then turn them out onto racks. Remove the paper and allow to cool completely before frosting. Spread the Divinity Icing between the layers and all over the top and sides of the cake.
Pour the egg whites and salt into a stand mixer fitted with a whip attachment. Beat the egg whites until smooth but not stiff; they should not form stiff peaks.
In a large saucepan, mix the sugar, 3/4 cup water, corn syrup and vinegar. Stir until the sugar dissolves, then heat the mixture until it reaches the hard ball stage (265 degrees F on a candy thermometer), about 12 minutes. When done, the syrup will spin a long thread when poured off the edge of a spoon. Remove the syrup from the heat and stir in the mini marshmallows. The mixture will be foamy. With the mixer running at high speed, stream the syrup into the egg whites. Beat well, and then beat in the vanilla.