Whisk the soy sauce, gochujang sauce, tomato paste, peanut butter, water, brown sugar, sesame oil, and minced garlic in a small bowl or shake together in a jar until it forms a thick sauce.
Cook the ground chicken in a large skillet over medium-high heat until browned. Season generously.
Boil noodles according to package directions until just softened. Drain and set aside.
Add the cooked chicken, cooked noodles, and the prepared sauce to the skillet. Toss to combine over medium-high heat until the noodles are heated through.
Add broth or water, a little at a time, to thin the sauce to your desired sauciness. Toss well to coat everything evenly.
Serve immediately, topped with your favorite fresh herbs, scallions, chili oil, or sesame seeds for extra flavor and texture.