Preheat oven to 350 degrees.
Whisk the eggs and milk in a medium large bowl and season with salt and pepper.
Add the spinach and kimchee and stir.
Heat the oil on a 6-9 inch oven safe skillet (smaller if want a thicker frittata, larger for a thinner one) over medium high heat. Make sure oil coats entire surface and then pour in the egg mixture.
Cook for 1 or 2 minutes, gently stirring the egg mixture and pushing away from the edges.
Add the goat cheese evenly across the top.
Transfer pan to the oven and cook 4 to 6 minutes (depending on how thick the frittata is) until eggs are just firm.
Let sit at least five minutes before trying to pull the sides away from the pan, gently, with a spatula.
Cut into wedges and serve.
Makes one 8 inch frittata or 3-4 servings