Crisp the Bacon: Place the bacon pieces in a cold dry pan and bring it up to medium heat. Let them cook for 3 to 4 minutes until the fat has fully rendered and the edges are golden and crisp but the centers are still slightly chewy. Transfer to a paper towel and leave the pan on low heat with the rendered fat still in it.
Sauté the Garlic Butter Mushrooms: Add the butter and grated garlic directly into the bacon fat in the same pan. Let the garlic sizzle for 20 to 30 seconds until it smells nutty and fragrant, not brown. Add the sliced mushrooms in a single layer and leave them completely untouched for 2 full minutes so they develop a golden, caramelized edge. Toss once, season with a pinch of salt and cracked pepper, then remove the pan from the heat.
Make the Egg Yolk Sauce: In a small bowl, whisk together the egg yolk, heavy cream, grated parmesan, and mayonnaise until the mixture is smooth, thick, and pale, like a loose, glossy aioli. Set it aside at room temperature.
Boil the Noodles: Bring a small pot of water to a full, rolling boil. Add the buldak noodles and cook for exactly 3 minutes, stirring once at the halfway mark. Before draining, scoop out 3 tablespoons (45ml) of the starchy cooking water and set it aside. Drain the noodles completely and return them to the pot off the heat entirely.
Build the Sauce: Add both sauce packets from the buldak pack over the hot drained noodles and stir to coat evenly. Pour the egg yolk mixture over the top and immediately toss using chopsticks or tongs, working quickly and continuously so the heat from the noodles gently cooks the egg into a silky, clinging sauce. If the sauce looks too thick after 30 seconds of tossing, add the reserved cooking water one tablespoon at a time until the sauce coats every strand without pooling at the bottom.
Plate and Finish: Transfer the noodles immediately to a bowl. Pile the garlicky mushrooms on top, scatter the crispy bacon across, then add the fresh chives or scallions. Finish with a generous grating of extra parmesan and a solid crack of black pepper. Add the halved soft-boiled egg and a few drops of sesame oil if using, and serve right away.