Bring a large pot of water to a boil. Add the udon noodles and cook according to the package instructions, usually 3-5 minutes for fresh or frozen noodles. Once cooked, drain and rinse under cold water to stop the cooking process and set aside.
In a small bowl, whisk together the freshly squeezed orange juice, orange zest, soy sauce, honey, and chili paste until well combined. Set this vibrant sauce aside to infuse flavors while you prep the rest.
Heat 1 tablespoon of vegetable oil in your skillet or wok over medium-high heat. Add the thinly sliced beef in a single layer and cook until browned on both sides, about 2-3 minutes per side. Remove the beef from the pan and set aside.
Add the remaining tablespoon of oil to the pan. Toss in the minced garlic and ginger, sautéing until fragrant—about 30 seconds. Then add the sliced bell pepper and julienned carrot, cooking until just tender but still crisp, roughly 3-4 minutes.
Return the cooked beef to the pan with the vegetables. Pour the orange sauce over everything and stir well to coat. Let it simmer for 1-2 minutes to thicken slightly and marry the flavors.
Add the drained udon noodles directly to the skillet. Using tongs or a spatula, gently toss and stir for another minute until the noodles are heated through and fully coated in the sweet and spicy sauce.
Remove from heat and sprinkle generously with sliced green onions and toasted sesame seeds. Serve immediately for a hearty, flavor-packed meal.
