In a 12-ounce microwave-safe mug, whisk together the flour, sugar, cocoa powder, baking powder, and salt with a fork until no lumps remain.
Add the milk, oil, and vanilla extract to the dry ingredients. Stir until just combined and smooth, about 15-20 strokes.
Fold in 1 tablespoon of chocolate chips and 1 tablespoon of crushed graham crackers, reserving the rest for topping. Let the batter rest for 30 seconds.
Microwave on high power for 60-75 seconds, depending on your microwave wattage. The cake should rise significantly and the center should look just barely set with a slight jiggle.
Immediately top the hot cake with the remaining chocolate chips, crushed graham crackers, and tear the marshmallow into pieces to distribute over the surface.
Return to the microwave for 10-15 seconds just until the marshmallow puffs and softens. Alternatively, use a kitchen torch to toast the marshmallow topping.
Let cool for 1 minute before eating directly from the mug with a spoon. The center will be molten, so be careful with your first bite.