Stir Fry Noodles with Chicken and Vegetables

rice noodles

coconut oil or light flavored olive oil ((divided))

low-sodium soy sauce, plus 2 tablespoons ((divided))

chili paste

light brown sugar

minced fresh ginger

garlic, minced

thinly sliced carrots, about 2 medium carrots

broccoli florets, cut bite-size

large mushrooms, sliced thin, about 2 cups

green cabbage, very thinly sliced

lbs chicken thighs, cut into bite-size pieces

cornstarch