Bring a large pot of water to a boil. Add the wheat noodles and cook according to package instructions until tender but still slightly firm. Drain and rinse under cold water. Set aside.
Heat the vegetable oil in a wok or large frying pan over medium heat. Add the garlic, ginger, and half of the green onions. Stir-fry for 1-2 minutes or until fragrant.
In a small bowl, mix together the hoisin sauce, sesame paste, soy sauce, rice vinegar, brown sugar, and chili flakes (if using).
Add the sauce to the wok and stir until well combined. Simmer for 2-3 minutes or until the sauce has thickened slightly.
Add the cooked wheat noodles to the wok and stir gently to coat with the sauce.
Divide the noodles among serving bowls and top with sliced cucumber and the remaining green onions.
Serve hot, garnished with extra chili flakes and salt to taste.