Heat the vegetable oil in a large skillet or wok over medium heat.
Add the chopped onion and sauté for 3-4 minutes until it becomes translucent.
Stir in the minced garlic and grated ginger, cooking for an additional 1 minute until fragrant.
Add the bite-sized pieces of chicken thighs to the skillet, cooking for about 5-6 minutes, until they are no longer pink.
Stir in the red curry paste, ensuring that it coats the chicken well.
Pour in the coconut milk, and then add the bell pepper, broccoli florets, soy sauce, fish sauce (if using), and sugar. Stir to combine.
Bring the mixture to a gentle simmer, cover, and cook for 15 minutes, stirring occasionally.
Taste and adjust seasoning, adding more soy sauce or sugar if desired.
Serve the coconut curry chicken over cooked rice, garnished with fresh cilantro and lime wedges on the side.