Rinse the jasmine rice under cold water until the water runs clear. Place it in a medium saucepan with 3 cups of water and a pinch of salt. Bring to a boil, then reduce heat to low, cover, and simmer for 15 minutes until the rice is tender and all water is absorbed.
While the rice cooks, heat the vegetable oil in a large skillet over medium heat. Add the diced onion and cook for 3 minutes until it starts to soften.
Stir in the minced garlic and grated ginger. Cook for 1 minute until fragrant.
Add the chicken pieces to the skillet. Cook for 5 minutes, stirring occasionally, until the chicken is no longer pink on the outside.
Sprinkle the mild curry powder over the chicken and stir to coat everything evenly. Cook for 1 minute more.
Pour in the coconut milk and chicken broth. Add the salt and stir well. Bring the mixture to a gentle simmer, then reduce heat to low and cook uncovered for 12 minutes until the chicken is fully cooked and the sauce has thickened slightly.
Remove the rice from heat and let it rest covered for 5 minutes. Fluff with a fork before serving.
Spoon the curry over portions of steamed rice. Top with chopped cilantro and serve with lime wedges on the side.