Bring a large pot of salted water to a boil. Add the pasta noodles and cook for 8 - 10 minutes (or until al dente).
Drain the pasta and reserve 1/2 cup of the starchy cooking water. Toss the pasta with 1 tablespoon of olive oil and set aside.
Meanwhile, in a large skillet, cook chopped pancetta/bacon over medium heat until slightly crisp (about 3 minutes), remove, and drain on a paper towel. Leave the remaining fat in the skillet.
Add a tablespoon of olive oil to the skillet. Add the onion and stir well to coat with fat. Cook until translucent. Then turn the heat down and add the garlic, and cook for about one minute. If using white wine, add it now and let it reduce a bit.
Stir in the kimchi and bacon and cook for several minutes. Then add the milk and cream, and cook for another minute or so. Now add the kimchi juice and continue cooking over low heat for several minutes until the sauce reduces.
Add the hot, drained spaghetti to the skillet and toss for two minutes with tongs to coat the strands evenly. Add more olive oil if it seems dry or sticky.
Combine the beaten eggs and Parmesan together in a mixing bowl, stirring well. Remove the pan from heat and pour the egg/cheese mixture into the pasta, whisking quickly until the eggs thicken but do not scramble. Toss to coat and heat through.
Thin out the sauce with a bit of reserved pasta water, until it reaches desired consistency.
Season the pasta with freshly ground black pepper and salt. Garnish with chopped parsley and more grated Parmesan.