Who were the earliest people born in East Asia to travel to Europe write detailed chronicles of their experiences and bring them back to East Asia?
The closest parallel to Marco Polo is Rabban Bar Sauma, whose own journey westward was roughly contemporaneous with Polo's. He was born in the vicinity of modern day Beijing around 1220 and eventually became a member of the Church of the East (aka "a Nestorian Christian"). He and one of his students undertook a pilgrimage to Jerusalem in the 1260s but got stuck in Mongol-controlled Baghdad due to the ongoing war conquest of the Middle East and the dangers this posed to travel. When they arrived, the Church of the East had just elected a new Patriarch and they ended up staying so long (into the 1280s), that Bar Sauma's student eventually became the Patriarch of the Church when the previous one died.
Shortly after this, the leader of the Ilkhanate, Arghun Khan, set Bar Sauma and others on a diplomatic mission to Europe in an attempt to cement a Franco-Mongol alliance. He met with the Byzantine emperor, the Pope, and the kings of England and France (both in modern-day France). Ultimately, though, while he got a decent reception in Europe, Bar Sauma was unsuccessful in securing strong commitments to the Franco-Mongol alliance. He returned to Baghdad, where he lived the rest of his life.
This map shows his overall route.
For much of China's history, exploration and travel was done much more in a maritime manner than over land. This made it difficult to make it to Europe as maritime explorers would either have to circle around the Cape of Good Hope or leave their ships and go over land at some point.
However, there were some Chinese explorers/ambassadors that made it pretty far West. The best example is Gan Ying who was a Han official of the late 1st century who made it to Roman Syria, potentially visiting the Mediterranean Sea. His experiences are partially chronicled in the Book of the Later Han (Hou Han Shu).
Hi, if you're interested in some past related posts, check out this one here - it contains a round-up of posts as well as some additional answers