A photo like it (a hand drip through a cone) · GorillaWarfare (CC BY-SA 1.0) via Wikimedia Commons · source
The cup of Tokyo's old coffee houses like Café de l'Ambre and Kayaba: darker roasts, a flannel or paper drip poured a few drops at a time, and a thick, sweet, round cup served in fine china.
20 g (3 heaped tbsp) medium-dark to dark roast beans, ground medium
Water just off the boil, cooled to 85 to 88°C (185 to 190°F)
A flannel drip filter (nel drip) or a paper cone, and a gooseneck kettle
How to make it
Cool the water (2 min): Boil it, pour it into the kettle, and let it rest until 85 to 88°C. Dark roasts get bitter with very hot water.
Wet (30 sec): Rinse the filter. Add the coffee and dot water over it, drop by drop, from the centre outward, just until the surface darkens. Wait 30 seconds while it swells into a dome.
Drip (3 to 4 min): Pour in a thin thread, in small circles in the centre only, never touching the filter. Keep the dome from falling. Pour about 150 ml through in total, slowly.
Finish: Take the dripper away before the last of the water drains through; the last drops carry bitterness. Warm the cup with hot water first and pour in.
Serve: Black, in a thin china cup, perhaps with a slice of thick toast or a pudding, as the kissaten do.
Tips
Flannel filters need care: rinse, keep it in water in the fridge, never let it dry.
Café de l'Ambre's trick is aged beans and a very slow pour; any good dark roast and patience gets you close.
A Tokyo coffee house is a place to sit for an hour. Make this when you have one.