Heat the vegetable oil in a large pot over medium heat. Add the diced onion and sauté until translucent, about 5 minutes. Stir in the minced garlic and grated ginger, cooking for an additional minute until fragrant.
Season the chicken thighs with salt and pepper. Add them to the pot, browning on both sides for about 5 minutes.
Stir in the red curry paste, mixing well with the chicken and onion mixture.
Pour in the coconut milk, soy sauce, brown sugar, and chicken broth. Bring the mixture to a simmer.
Reduce the heat to low, cover the pot, and let it simmer for 30 minutes, stirring occasionally.
After 30 minutes, add the sliced red bell pepper and snap peas. Cook for an additional 10 minutes until the vegetables are tender and the chicken is cooked through.
Taste and adjust seasoning with more salt and pepper if needed.
Serve hot, garnished with fresh cilantro and lime wedges on the side.