01 - Boil 1.5 liters of water with 1 tablespoon of salt. Add pasta and cook until al dente, approximately 1 minute less than package directions. Drain, reserving 1/4 cup of the pasta water, and set aside.
02 - Heat 1 tablespoon of butter and 1 tablespoon of olive oil in a large nonstick or cast iron skillet over medium-high heat. Add minced garlic and sauté until fragrant, about 30 seconds.
03 - Add the drained pasta to the skillet, spreading it evenly. Pour in the reserved pasta water, soy sauce, and half of the sliced scallions. Drizzle with sesame oil and sprinkle with black pepper.
04 - Gently press the pasta into the skillet. Pour the vegetable or chicken stock around the edges of the skillet. Add the remaining butter and olive oil around the sides. Evenly sprinkle grated Parmesan cheese over the pasta, if using.
05 - Reduce heat to medium, cover the skillet, and cook for 8–10 minutes, or until the bottom achieves a deep golden crust and most of the liquid has evaporated.
06 - Remove the lid and increase heat to medium-high. Continue cooking for 2–3 minutes to further crisp the bottom. Loosen the edges with a spatula. Carefully invert the pasta onto a large platter or slide it out, presenting the crispy side upwards.
07 - Top with the remaining sliced scallions and toasted sesame seeds. Slice into wedges and serve immediately.