Heat the vegetable oil in a large skillet or deep pan over medium-high heat. Add the diced onion, minced garlic, and grated ginger. Sauté for 2-3 minutes until fragrant and the onion becomes translucent.

Add the chicken pieces to the pan, seasoning with salt and black pepper. Cook for 4-5 minutes, stirring occasionally, until the chicken is browned on all sides but not fully cooked through.

Stir in the yellow curry paste and turmeric powder. Cook for 1 minute to toast the spices, releasing their flavors and coating the chicken evenly.

Add the sliced bell pepper and carrots. Stir to combine, then pour in the coconut milk, chicken broth, fish sauce, lime juice, and brown sugar. Bring the mixture to a gentle boil.

Rinse the jasmine rice under cold water until the water runs clear, then stir it into the pan. Reduce the heat to low, cover the pan with a lid, and let it simmer for 20-25 minutes. Stir occasionally to prevent sticking, and check if the rice is tender and has absorbed most of the liquid.

Once the rice is cooked and the chicken is tender, remove from heat. Let it sit covered for 5 minutes to allow flavors to meld.

Garnish with fresh chopped cilantro and serve with lime wedges on the side.