筍 combines 竹 (bamboo) with 旬, which likely contributes the sound. The character specifically refers to bamboo shoots.
Meaning mnemonic
The top 竹 is bamboo, and the bottom 旬 looks like a wrapped bundle. Imagine a tender bamboo shoot wrapped in its protective sheath, ready to be harvested.
Reading mnemonic
For ジュン, picture a bamboo shoot growing in June: June -> ジュン, and the shoot is ready to eat.