1.In a medium pot fill halfway with water and bring it to a boil on high heat. Turn the heat off and add in the frozen udon. Mix the noodles well to separate then drain in a colander.
2.In a small pan on low heat add 1 teaspoon oil then crack two eggs into the pan and cook until the egg whites are firm and egg yolks are runny.
3.Meanwhile, in a medium pan, add in 2 teaspoons oil and turn the heat to medium high. Add in mushrooms and kimchi, and saute for 2-3 minutes. Once kimchi is fragrant, add soy sauce, gochugaru, and dashi granules and saute for another 2 minutes.
4.Pour in milk and udon noodles and cook for another 3 minutes, mixing well. Garnish with green onions and sesame seeds then top with the two eggs. Serve immediately.