Preheat your oven to 350F/175C and lightly grease and flour a 10x15 jelly roll pan (or spray with baking spray).
In a medium-sized saucepan, combine butter, water, and cocoa powder. Turn heat to medium low and stir occasionally until butter is melted.
Increase heat to medium-high and (stirring frequently) bring to a rolling boil. Remove from heat and allow to cool for 15-20 minutes.
Meanwhile, whisk together flour, sugar, baking soda, salt, and instant coffee (if using) in a large bowl. Make a well in the center and add sour cream, eggs, and vanilla extract. Whisk together sour cream/eggs/vanilla in the well, then use a spatula to combine all ingredients in the bowl (mixture will be thick).
Add slightly cooled chocolate mixture to the flour mixture and stir until well-combined (be careful, chocolate mixture will still be a bit hot).
Pour batter into prepared pan and carefully (don’t spill!) transfer to 350F (175C) oven. Bake for 20-25 minutes or until toothpick inserted in center comes out clean or with a few moist crumbs, but while cake is baking measure out your marshmallows and prepare frosting.
Prepare frosting by combining milk and butter in large heatproof bowl and microwave, stirring every 15 seconds, until melted and mixture is warm. Sift in cocoa powder and whisk until combined.
Gradually sift in powdered sugar and whisk until smooth. Stir in vanilla extract.
Once cake has finished baking, pour mini marshmallows evenly over the top and very gently press them against the surface of the cake (don’t smash the cake!). Pour chocolate frosting evenly over the cake.
Allow cake to cool and frosting to set, about 1-2 hours, before cutting and enjoying.