Vegetable Yaki Udon Noodles

Name: Vegetable Yaki Udon Noodles
Ingredients: 2 (or 400g) packets udon noodles (frozen or pre-cooked ); 2 tbsp vegetable oil divided; ½ lb tofu (or protein of your choice); ½ yellow onion (sliced); 1 cup cabbage shredded; 2 cloves garlic (minced); ¼ cup carrot cut in matchsticks½; 3 (3-4) shiitake mushrooms (sliced (rinse them in water before using)); 2 green onions (chopped (some reserved for garnish)); ½ tbsp sesame seeds (toasted (green onions, and/or bonito flakes for garnish, optional)); 2 tbsp dark soy sauce; 2 tbsp vegan oyster sauce; 1 tbsp mirin (or sake); 1 tbsp brown sugar (optional); 2 tbsp water; 1 tsp red pepper flakes (optional)