Cook the udon noodles according to package instructions. Drain and set aside.
In a large skillet, heat the vegetable oil over medium heat. Add the minced garlic and grated ginger, sautéing for about 1 minute until fragrant.
Add the broccoli, bell peppers, and snap peas to the skillet. Stir-fry the vegetables for about 5-7 minutes until they are tender but still crisp.
In a bowl, whisk together the gochujang, coconut milk, soy sauce, rice vinegar, and sesame oil until smooth.
Pour the sauce over the cooked vegetables in the skillet and stir to combine. Add the cooked udon noodles and toss everything together until the noodles are well coated with the sauce.
Cook for an additional 2-3 minutes, allowing the noodles to heat through.
Serve hot, garnished with sliced green onions and sesame seeds.