In a large saucepan, heat the olive oil (or cooking fat) over a medium heat.
Cook the scallions, garlic, and ginger, stirring frequently, until softened (about 5 minutes).
Add the carrot, red bell pepper, jalapeño, and mushrooms, and cook until softened (about 3-4 minutes).
Add the chicken, chicken stock, coconut milk, and fish sauce.
Bring the soup to a boil then reduce to a simmer and cook until the chicken is cooked through (15 to 20 minutes).
Remove the chicken from the soup. Shred it into chunks and return to the pot.
Stir in the lime zest, the fresh herbs, and salt and pepper to taste, and remove from the heat.
Garnish each bowl with a lime wedge to serve.