Cook the udon noodles according to the package instructions. Drain and cover to keep warm while you prepare the stir-fry vegetables.
Start by cutting all your veggies. Heat the oil in a large skillet over medium heat. Once hot, add the onion and red bell pepper and cook for about 5 minutes. Next, add the carrots, pak choy, and green onions. Cook for another 5 minutes, stirring regularly to cook evenly.
In the meantime, whisk together the soy sauce, satay paste, coconut sugar, lime juice, and garlic.
Add the cooked noodles to the skillet as well as the sauce. Stir to coat and cook for about 2 minutes, stirring regularly.
Divide into bowls and serve immediately! These noodles will keep for up to 2 days in the refrigerator, and are also delicious served cold.