Heat a large pot over medium-low heat and add the coconut oil. Stir in the onions, garlic, peppers, carrots and ginger with a pinch of salt and pepper. Cook until the vegetables have slightly softened, about 5 minutes. Stir in the curry paste and cook for 5 minutes, stirring occasionally, scraping the bottom.
Stir in the chicken stock, coconut milks, snap peas and chicken. Increase heat and bring the mixture to a boil, then reduce the heat to low, cover and cook for 5 minutes. Taste and season additionally if needed.
Toss in the zoodles from one or two zucchini squash - however many you would like! Serve immediately with some green onions and cilantro on top.
Note: this reheats well really, but the zoodles can get mushy! I do suggest making zoodles and keeping them in your fridge, and adding just enough to the hot soup each time you heat it so they stay crisp.