Slice the chicken breast fillets thinly. Slice the carrots and mushrooms into thin slices, and finely chop garlic and chili. Split the lemongrass in half through the middle lengthwise, and chop into long sticks.
Heat the vegetable oil in a large pot, then add the chicken slices and cook until the meat is white. Remove it from the pot and set it aside.
In the same pot, saute the lemongrass, chili and garlic for a minute.
Add curry paste, carrots and mushrooms. Saute for a minute or two to allow the vegetables to heat up slightly on the outside.
Add coconut milk and vegetable or chicken stock, and bring the soup to a boil then down to a simmer. Allow it to cook for 5-10 minutes, or until the carrots have cooked through.
As lemongrass is only added for flavour, but is not very pleasant to eat, we want to remove them from the soup. Use a spoon or tongs to fish the pieces out.
Add the cooked chicken along with fresh coriander and cooked noodles. Let the soup sit for a minute or two so that the chicken and noodles can reheat and absorb some of the flavours of the soup.
Serve it while still warm, optionally topped with your choice of garnish.