Heat the oil in a large saucepan and add the onions, garlic and ginger. Cook over a medium heat, stirring occasionally, for 3 - 4 minutes.
Stir in the curry paste and cook for 1 minute. Add the chicken and cook for 2 minutes.
Add the Kaffir Lime leaves, lemongrass and pour in the coconut milk and bring to the boil. Reduce the heat and simmer gently, stirring occasionally, for about 15 minutes.
Add the pepper, broccoli and mushrooms, soy sauce, fish sauce, lime juice and brown sugar and cook for 5 minutes. Stir well.
Stir in the cornflour and season. Cook for 5 minutes. Remove the kaffir lime leaves and lemongrass.
Use a spoon to remove any oil that rises to the top. Season to taste and serve in bowls topped with coriander leaves and a side of rice or quinoa and veg.