Rinse the cucumber and lay it on a cutting board. Whack it firmly along its length with a rolling pin (or the flat side of a knife) until it cracks open in several places.
Tear or chop the smashed cucumber into rough 3 cm bite-sized pieces — jagged edges are what you want.
Remove the pit from the umeboshi and roughly chop the flesh into a coarse paste on the cutting board.
Put the cucumber into a mixing bowl. Add the chopped umeboshi, the full pack of katsuobushi, and 1/2 teaspoon of mentsuyu.
Toss well until every piece of cucumber is coated in seasoning. Taste and adjust — more umeboshi for salt, more mentsuyu for depth.
Transfer to a small bowl and serve immediately. For a slightly deeper flavour, chill for 5 minutes before serving.