Easy Bulgogi Beef Udon Stir Fry

Name: Easy Bulgogi Beef Udon Stir Fry
Ingredients: 2 packs (17-oz./500g) udon noodles (preferably frozen (see notes below)); 2 tbsp vegetable oil; 300 g sliced beef (rib eye or top sirloin); 1/2 medium onion (sliced); 40 g carrot (julienned); 30 g shiitake mushrooms (or any mushroom of choice, sliced); 2 green onions (chopped); 1 tbsp oyster sauce (or to taste); toasted sesame seeds and green onion (for garnish); 4 tbsp soy sauce; 2 tbsp mirin; 1 tbsp sesame oil; 1 tbsp honey; 1 tbsp brown sugar; 6 cloves garlic (minced); 1/4 tsp black pepper