Place the fresh udon noodle packets in hot water for several minutes, or rinse them under hot running water, until the strands begin to loosen.
Gently separate the noodles without pulling or forcing apart any compacted sections, as fresh udon can break easily.
Drain thoroughly and reserve for later.
Add the gochugaru, vegetarian oyster-style sauce, low-sodium soy sauce, sugar, sesame seeds, sesame oil, and 1 tablespoon of water to a small bowl.
Stir thoroughly until the sugar has dissolved and the mixture has a smooth, even consistency.
Taste the sauce and adjust the amount of chili powder according to the preferred level of heat. Set aside.
Warm a large wok or nonstick skillet over medium-high heat, then add 1 tablespoon of the neutral oil.
Once the oil is hot, place the crumbled tofu in the pan. Break apart any remaining large pieces while it cooks.
Leave the tofu undisturbed for 3 to 4 minutes, allowing the underside to become golden and crisp. As moisture evaporates, the tofu should develop a dry, finely crumbled texture.
Pour in the dark soy sauce and stir until the tofu is evenly seasoned.
Continue cooking for another 3 to 4 minutes, or until the tofu is thoroughly browned and dry. Move it to one side of the pan.
Pour the remaining tablespoon of neutral oil onto the vacant side of the pan.
Add the minced garlic and sauté over medium heat for approximately 30 seconds, just until aromatic.
Stir in half of the sliced green onions and cook for 1 minute.
Add the sliced shiitake mushrooms and stir-fry for 2 to 3 minutes, until tender and lightly browned.
Transfer the drained udon noodles to the pan containing the tofu, mushrooms, garlic, and green onions.
Pour the prepared sauce over the noodles, then toss carefully until every strand is evenly coated and the ingredients are well distributed.
Cook over medium-high heat for 2 to 3 minutes.
When the noodles appear dry or require additional softening, gradually incorporate 2 to 4 tablespoons of water, mixing well after each addition.
Taste and add a small amount of salt and black pepper when desired. A light drizzle of additional sesame oil may also be added for a fuller finish.
Remove the pan from the heat.
Scatter the reserved green onion slices over the noodles and add an optional sprinkling of sesame seeds.
Serve immediately while hot.