Get tteok, you can also get a set that includes the sauce pack. Another option is to make it with the ramen packet and add tteok.
have the tteock soaking in the water while you prepare the other parts of the dish.
Bowl water in a pan about 2-2 1/5 cups of water
when the water has boiled add the tteok and whatever sauce or seasonging or your choosing (ramen packet, sauce packet, your own sauce with gochujang, etc), wait until it is soft (see if you can stick a chopstick through it)
when teh tteok is ready, add your instant noodles and after one minute, ass your meat and your mushrooms.
when your meat and noodles seem cooked, add your cheese and some scallion at the end and wait a little until melted. Then serve.