Heat vegetable oil in a large pan or wok over medium-high heat. Add the bruised lemongrass, minced garlic, and grated ginger. Stir-fry for about 30 seconds until fragrant.

Add the sliced onion to the pan and cook for 3-4 minutes until softened and translucent. Push the aromatics to one side and add the red curry paste to the cleared space. Fry the paste for 1-2 minutes until it darkens slightly and becomes very fragrant.

Add the chicken pieces to the pan, stirring to coat them with the curry mixture. Cook for 5-6 minutes, turning occasionally, until the chicken is mostly white on all sides but not fully cooked through.

Pour in the coconut milk, stirring to combine with the curry base. Add fish sauce, brown sugar, and kaffir lime leaves if using. Bring the mixture to a gentle boil, then reduce heat to maintain a steady simmer. Simmer for 8-10 minutes until the chicken is cooked through and the sauce has thickened slightly.

Stir in the bell pepper and green beans. Continue simmering for 5-6 minutes until the vegetables are tender-crisp and bright in color. Taste and adjust seasoning with salt or additional fish sauce. Remove from heat and stir in fresh Thai basil leaves.

Let the curry rest for 2-3 minutes before serving to allow the flavors to meld and the sauce to reach the perfect consistency.