Bring a large pot of water to a boil for the noodles.
Heat 1 tablespoon of olive oil in a large pan over medium-high heat. Once hot, add the veggies and season with a generous pinch of kosher salt and black pepper. Cook for 6-8 minutes, stirring every couple of minutes, until the veggies are tender and browning in spots. Transfer to a bowl and set aside.
Add the ground chicken to the same pan. Cook on one side for 3-4 minutes until golden brown before breaking apart and fully cooking.
While the chicken cooks, mix the gochujang, hoisin, vinegar, coconut aminos, toasted sesame oil, and garlic together.
Add the sauce to the cooked chicken and stir everything together. Cook until the sauce coats the chicken and the garlic is fragrant, about a minute. Reduce the heat to low and start cooking the noodles.
Cook the noodles for 4 minutes (or to al dente according to the instructions on the noodles you use). Reserve about a cup of the water before draining the rest.
Toss the chicken, veggies, and cooked noodles together, using the reserved water as needed to bring everything together. (I used about 1/2 cup.)
Serve with pickled cucumbers or kimchi, toasted sesame seeds, and sliced green onion, if desired.