In a medium bowl, combine the thinly sliced beef with 1 tbsp soy sauce, 1 tbsp cornstarch, 1 tsp sesame oil, and 1/2 tsp black pepper. Toss well to coat. Let marinate at room temperature for at least 10 minutes while you prepare other ingredients.

In a small bowl, combine 2 tbsp soy sauce, 1 tbsp oyster sauce, 1/2 tsp dark soy sauce (if using), 1 tsp sugar, 1/4 tsp white pepper, 2-3 tsp freshly cracked black pepper, 3 tbsp water or chicken broth, and 1 tsp cornstarch. Whisk until smooth and set aside.

Cook udon noodles according to package instructions. If using fresh noodles, rinse under hot water to separate. If frozen, boil until tender. Drain thoroughly and set aside.

Heat 1 tbsp vegetable oil in a large wok or skillet over high heat until shimmering. Add the marinated beef in a single layer (cook in batches if necessary to avoid overcrowding). Stir-fry for 2-3 minutes until browned on all sides and mostly cooked through. Remove the beef from the wok and set aside.

Add the remaining 1 tbsp vegetable oil to the wok. Add minced garlic and grated ginger, stir-fry for 30 seconds until fragrant. Add the sliced yellow onion and green bell pepper. Stir-fry for 3-4 minutes until vegetables are crisp-tender.

Return the cooked beef to the wok with the vegetables. Add the drained udon noodles. Give the prepared black pepper sauce a quick whisk again, then pour it over the noodles, beef, and vegetables.

Toss everything quickly to coat evenly, ensuring the sauce thickens and coats all ingredients, about 1-2 minutes. The sauce should become glossy.

Remove from heat. Garnish with chopped green onions and sesame seeds (if using). Serve immediately.