Begin by cooking the udon noodles according to package instructions. Once cooked, drain and set aside.
Heat the sesame oil in a large skillet or wok over medium heat. Add the minced garlic and sauté for about 30 seconds until fragrant.
Add the julienned carrot and sliced bell pepper to the pan. Stir-fry for 2-3 minutes until they begin to soften.
Mix in the shiitake mushrooms and bok choy, stir-frying for an additional 2 minutes until the bok choy is wilted and mushrooms are tender.
Add the cooked udon noodles to the skillet and gently toss everything together.
In a small bowl, whisk together the soy sauce, mirin (or rice vinegar), and sugar, then pour it over the stir-fried noodles and vegetables. Stir until everything is evenly coated and cooked through, about 2-3 minutes.
Season with salt and pepper to taste. If desired, toss in the chopped green onions for added flavor.
For a special touch, serve each portion with a fried sunny-side-up egg on top and sprinkle with sesame seeds.
Notes
Serve in deep bowls, topping with a fried egg and a sprinkle of sesame seeds.