In a large skillet or wok, heat the vegetable oil over medium heat. Add the chicken pieces and cook until browned, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the chopped onion and sauté until translucent, about 3-4 minutes. Stir in the minced garlic and grated ginger, cooking for an additional minute until fragrant.
Add the red curry paste to the skillet, stirring well to combine with the onion mixture. Cook for 2 minutes to release the flavors.
Pour in the coconut milk and chicken broth, stirring to combine. Add the fish sauce and brown sugar, then bring the mixture to a simmer.
Return the browned chicken to the skillet and add the sliced red bell pepper and snap peas. Simmer for 10-15 minutes until the chicken is cooked through and the vegetables are tender.
Stir in the baby spinach and lime juice, cooking for an additional 2 minutes until the spinach is wilted.
Serve the curry over cooked jasmine rice and garnish with fresh cilantro.