Heat 2 tablespoons of vegetable oil in a large skillet or wok over medium-high heat, allowing it to shimmer.

Add 1 minced garlic clove and 1/2 teaspoon of grated ginger to the hot oil, stirring constantly for approximately 30 seconds.

Toss in 1/2 sliced onion and sauté for 2-3 minutes until translucent.

Incorporate 1/2 cup shredded cabbage, 1 small julienned carrot, 1/4 cup sliced mushrooms, and 1/2 sliced bell pepper into the skillet and stir-fry for about 3-4 minutes.

Gently fold in 2 portions of cooked udon noodles, making sure to break apart any stuck pieces and warm them through for about 1-2 minutes.

Pour in a mixture of soy sauce, oyster sauce, mirin, and a pinch of sugar over the noodles and vegetables, stir-frying for an additional 2-3 minutes.

Remove from heat and serve hot, garnished with sliced green onions and sesame seeds.