Soak rice disks in luke-warm water for at least an hour.
In a stock pot, bring stock to a simmer and add ginger. Simmer for 15 minutes until fragrant.
Heat a cast iron pan to medium high heat. Add 3 tbsp vegetable oil. Let oil heat. Dust oxtails with flour then add to pan and sear on all sides. Remove from pan and set aside. To the same pan, add a splash of the stock and scrape any pieces off the bottom. Pour pan contents into the stock pot.
Remove the ginger from the stock pot and add in the wine. Bring to a simmer and cook for 5 minutes. Then add the leeks and cook until fragrant. About 3 minutes. Add the meat and cook for 1.5 to 2 hours, or until tender.
Add the rice cakes and cook for 10 minutes, or until just a bit firm. Add the kimchee and mushrooms and cook for another 2-3 minutes, or until rice cakes are chewy. Remove the pot from the heat and add in the chopped Chines greens.
Adjust seasoning with salt and white pepper. For extra spiciness, add the Korean chili flakes or more kimchee