Bring a large pot of water to a rolling boil, then add the udon noodles. Cook according to package instructions until just al dente, then drain and rinse under cold water to stop the cooking and prevent sticking.
While the noodles cook, prepare the vegetables: thinly slice the carrots into strips and chop the green onions. Mince the garlic and ginger to release their fragrant oils.
Heat the wok over medium-high heat until hot, then add the vegetable oil. Once shimmering and bubbling slightly, add the minced garlic and ginger. Cook for about 30 seconds until fragrant, with a warm, spicy aroma filling the air.
Add the sliced carrots to the wok, spreading them into a single layer. Let them cook undisturbed for 2-3 minutes until edges turn golden and caramelized, then flip and cook for another minute to develop a crispy, smoky texture.
Push the carrots to one side of the wok, then add the cooked noodles. Toss everything together with tongs or a spatula, stir-frying for 1-2 minutes to evenly coat the noodles with the aromatic flavors and heat through.
Pour the soy sauce over the noodles and vegetables, quickly tossing to coat evenly. Continue stir-frying for another minute until the sauce glazes the ingredients and the noodles develop a slight sheen.
Remove the wok from heat and sprinkle chopped green onions and toasted sesame seeds over the top. Toss briefly to combine, then transfer to serving bowls.
Serve immediately while hot, enjoying the perfect contrast of crispy carrots, tender greens, and chewy noodles in each flavorful bite.
