Heat vegetable oil in a large skillet or wok over medium heat. Once hot, add the sliced onion and sauté until translucent, about 5 minutes.
Add minced garlic and grated ginger to the skillet. Cook for 1-2 minutes until fragrant.
Stir in the red curry paste and cook for another minute to enhance the flavors.
Add the chicken pieces to the skillet, stirring well to coat them in the spice mixture. Cook for about 5-7 minutes until the chicken is no longer pink.
Pour in the coconut milk and chicken broth, then bring the mixture to a simmer.
Add the red bell pepper and snap peas to the skillet. Cook for 8-10 minutes, allowing the vegetables to soften but still retain some crunch.
Stir in the soy sauce, fish sauce, and brown sugar. Cook for an additional 2-3 minutes, adjusting seasoning with salt and pepper to taste.
Remove from heat and stir in lime juice just before serving.
Serve the curry over cooked rice and garnish with fresh cilantro.