I added an index for it (took about 15 minutes) with
CREATE INDEX ON hive_posts_cache((json::json->>'app'));
and then I could query like this
SELECT json::json->>'app' as app, author, permlink, body, created_at from hive_posts_cache where json::json->>'app' like 'busy%' order by post_id desc limit 100
RE: Tower: A REST API implementation on the top of Hivemind