Re: Chinese Cardamom (Lanxangia tsao-ko or in older texts, Amomum tsao-ko). Also referred to in English as Chinese black cardamoms or Chinese red cardamoms.
They are mainly used especially in Sichuan, Yunnan and neighbouring provinces and in Vietnam where they are an ingredient in the broth for phở. We border northern Vietnam and Yunnan so, they are readily available here, too. So they should be available in Chinese or S.E. Asian markets/stores. Here mainly used in hotpot broths.
In Chinese they are: 草果 (cǎo guǒ); in Vietnamese: thảo quả.
Here are some I bought in Guangxi recently. The largest is just over 1 inch long.