Sachyriel
Banned
I highly doubt that this could happen, unless you have a POD before 1000 in which Korea just comes short of being absorbed into China Proper.
Just look at the French, who invaded when their missionaries were tortured and executed. Although they did have initial successes, including the capture of numerous Joseon artifacts, they were eventually forced to withdraw. The Americans also failed in the Korean Expedition.
On the other hand, if Japan had more success in the Seven-Years War, they might have exported hwachas to Europe. However, the Japanese also failed miserably. Of course, you could argue that getting rid of Yi Sun-shin might result in a Japanese conquest of Korea, but he won so many battles in which he was outnumbered (Just look at the Battle of Myeongnyang. Yi only had 12 ships to Japan's 333), so Joseon would have been pressed hard to surrender. In fact, the king even ordered him to give up and join the army, yet he resolutely continued to fight on water with his salvaged navy. Also, although the Korean Army was disorganized, the navy was highly structured and had superior ships suited to the Korean geography. The best result that Japan would have is a partial conquest of the Korean Peninsula at best (Taking China was simply not an option).
To further highlight Korea's success at repelling invasions, it's worthy to note that it remained independent (although they were tributaries at times) from 2333 BC to 1910 AD, or a total of 4243 years. They weathered attempts from numerous empires, such as the Han, Tang, Mongols (a total of six invasions), Japan, Qing, France, and the United States, just to name a few.
However, the British might sign trade agreements (although highly doubtful) with Joseon in the 1800's, and weapons and culture might be transferred.
So the British can't do, Chinese can't do it, French can't do it and Japanese can't do it...
Is it because of the Hwachas?