Heat a large pot over medium heat and add the red curry paste, stirring for 1-2 minutes.
Add the diced chicken and cook until browned on all sides.
Pour in the coconut milk and stir to combine.
Add the fish sauce and brown sugar, mixing well.
Incorporate the bell peppers, broccoli, and carrots into the pot.
Bring the mixture to a gentle simmer and cover the pot.
Let it simmer for about 15-20 minutes until the vegetables are tender.
Stir occasionally to prevent sticking and ensure even cooking.
Once cooked, taste and adjust seasoning if necessary.
Serve hot, garnished with fresh basil and cilantro.