In a large pot of boiling salted water, add the udon noodles. Cook according to package instructions, usually about 3-4 minutes. Drain and rinse under cold water to stop the cooking process. Set aside.
In a large skillet or wok, melt the butter over medium heat. Once melted, add the minced garlic and red chili flakes. Sauté for about 1 minute until fragrant, making sure the garlic does not burn.
Add the broccoli, snap peas, and julienned carrot to the skillet. Stir-fry for about 4-5 minutes until the vegetables are tender but still crisp.
Add the drained udon noodles to the skillet. Drizzle with soy sauce and sesame oil. Toss everything together using tongs, ensuring that the noodles are well coated with the sauce and mixed with the vegetables.
Season with salt and pepper to taste. Continue to stir-fry for another 2-3 minutes to heat everything thoroughly.
Once everything is well combined and hot, remove from heat. Plate the udon noodles in bowls and sprinkle with chopped green onions and sesame seeds for garnish.
Notes
Adjust the chili flakes according to your spice preference.