Use a toothpick to carefully remove any trace of stems from the plums, being careful not to puncture the skin.
Soak the plums in cool water for a few hours or overnight. Drain well.
Fill a wide shallow bowl with vodka or spirits.
Add 30 ml (2 tablespoons) vodka to a quart-sized mason jar, close lid, and slosh around all the insides to sanitize it. Dump out vodka and set jar aside to air dry.
Measure salt, using 10% of the weight of the plums.
Rinse shiso leaves under cool water to remove dirt. Trim leaves, removing the woody stems. Sprinkle salt on the leaves, so they wilt slightly.
One small batch at a time, add plums to the bowl of spirits, rolling them around to sanitize them.
Build layers up in the jar. First, add salt (estimating the amount to add based on total batch size. Then add a layer of sanitized plums (letting them drip dry of spirits for a moment first). Then add a layer of now-wilted shiso leaves.
Repeat layering- salt, ume, shiso, until all ingredients are added to the jar.
Add weights (sanitize them first) to top of jar to encourage brine to form.
Cover tightly with lid.
The brine should form in the next few days so that the contents are completely submerged.