Preheat oven to 300°F. Grease three 8 inch round cake pans, line the bottoms with parchment paper circles, and lightly grease the parchment.
In a large bowl, whisk together flour, sugar, cocoa powder, baking soda, and salt until well combined.
Add eggs, milk, and vegetable oil to the dry ingredients and mix with a hand mixer or whisk until the batter is smooth.
Stir the vanilla bean paste into the hot water, then pour into the batter and mix until fully combined; the batter will be very thin.
Divide the batter evenly among the prepared pans and bake for 30 to 33 minutes, or until a toothpick inserted in the centers comes out with a few moist crumbs.
Cool the cakes in the pans for 5 minutes, then turn out onto wire racks, peel off parchment, and let cool completely.
When ready to assemble, preheat the oven to 350°F and line a rimmed baking sheet with parchment paper.
In a medium bowl, combine graham cracker crumbs, 1 1/2 tablespoons sugar, and melted butter, stirring until the crumbs are evenly moistened.
Spread the graham mixture in an even layer on the prepared baking sheet and bake for 8 to 10 minutes, until golden and crisp. Let cool completely and break into small crunch pieces.
Set the oven to broil on high. Line a baking sheet with parchment and spread the mini vanilla marshmallows in a single layer.
Broil the marshmallows for about 1 minute, watching closely, until deeply toasted on top. Remove from the oven and let cool completely, then break apart any large clumps.
For the marshmallow frosting, add 1 3/4 cups room temperature butter to a large mixer bowl and beat on medium speed until smooth and creamy, about 2 minutes.
Add the marshmallow fluff to the butter and beat until fully combined and smooth.
Beat in 3 cups of powdered sugar on low speed, then increase to medium until smooth. Add the remaining 3 cups powdered sugar and beat again until light and fluffy.
Gently fold the cooled toasted mini marshmallows into the frosting with a spatula. Set aside at cool room temperature.
For the ganache, place chocolate chips in a medium heatproof bowl. In a small saucepan, heat the heavy whipping cream over medium heat just until it begins to simmer, then immediately pour it over the chocolate chips.
Let the mixture stand for 3 to 5 minutes, then whisk until completely smooth and glossy. Let cool to a pourable but slightly thickened consistency.
For the outer vanilla frosting, beat 3/4 cup butter in a clean mixer bowl until smooth.
Add 1 1/2 cups powdered sugar and beat until combined and creamy.
Add vanilla bean paste and milk or cream, beat until smooth, then add the remaining 1 1/2 cups powdered sugar and beat until light and spreadable.
To assemble, place the first cooled cake layer on a serving plate or cardboard round. Spread a thin layer of vanilla frosting around the edge to form a dam.
Spoon about 6 tablespoons of chocolate ganache inside the dam and spread into an even layer.
Spread about 1 cup of marshmallow frosting over the ganache, staying inside the dam, then sprinkle about 1/2 cup graham cracker crunch evenly over the top and gently press in.
Place the second cake layer on top, press lightly to level, and repeat with another dam of vanilla frosting, 6 tablespoons ganache, 1 cup marshmallow frosting, and 1/2 cup graham crunch.
Top with the final cake layer. Refrigerate the stacked cake for about 30 minutes until the layers are set and stable.
Apply a thin crumb coat of the remaining vanilla frosting over the top and sides, chill for 15 minutes, then apply a final smooth layer of vanilla frosting.
Press the remaining graham cracker crunch around the bottom edge of the cake.
Pour or spoon some of the remaining ganache over the top of the cake, gently nudging it toward the edges to create natural drips.
Add extra mini vanilla marshmallows on top if desired and toast carefully with a kitchen torch until golden.
Refrigerate the finished cake until ready to serve. Serve slightly cool, not cold, and store leftovers covered in the refrigerator for up to 4 days.