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 for about 5-7 minutes until the vegetables are tender-crisp.
In a bowl, whisk together the gochujang, peanut butter, soy sauce, rice vinegar, honey (or maple syrup), and coconut milk until smooth.
Pour the sauce over the 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, stirring frequently, until everything is heated through.
Serve the noodles hot, garnished with sliced green onions and sesame seeds.