In a large pot, heat the vegetable oil over medium heat. Add the diced 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 sliced red bell pepper and carrots, cooking for another 3-4 minutes until they begin to soften.
Pour in the coconut milk and chicken broth, then stir in the red curry paste and soy sauce until well combined.
Bring the mixture to a gentle simmer, then add the chicken pieces. Cook for 10-12 minutes, or until the chicken is cooked through.
Stir in the baby spinach and cook for an additional 2 minutes until wilted.
Remove from heat and stir in the lime juice. Season with salt and pepper to taste.
Serve hot, garnished with fresh cilantro.