Bring a large pot of water (salted) to a boil over high heat.
In a medium bowl, whisk together egg yolk and egg until well blended. Stir in the cheese. Season with black pepper.
In a large Dutch oven over medium heat, add olive oil. Add pancetta and cook until crisp around the edges, about 7 – 8 minutes. Transfer the pancetta to a small bowl.
In the same Dutch oven, remove most of the fat, except for 2 tablespoons. Turn the heat to medium-low, add half of the kimchi (not all) and cook for 4 minutes.
In the meantime, cook the pasta until tender but still firm to the bite, stirring occasionally. Save ¾ cup pasta water. Drain pasta. Set aside.
Add ½ cup pasta water into Dutch oven with the kimchi. Bring to a boil over medium-high heat. Add cooked pasta. Stirring constantly and cook for about 2 minutes. Remove pot from heat.
Whisk in 2 tablespoons pasta water (not all) into the egg mixture. Then slowly pour into Dutch oven, stirring constantly, until cheese is melted. If needed, add a little more pasta water to thin out the sauce. Add the remaining kimchi and bacon. Stir well. Season with salt if needed.
Transfer pasta to serving plates. Sprinkle with black pepper and parmesan cheese. Serve immediately.