In a food processor, add the lemongrass, chilis, green onion, garlic, ginger, cilantro, cumin, pepper, soy sauce, salt, brown sugar, and oil. Process until smooth, about 1 minute, and set aside.
In a medium pan, cook the rice according to package instructions.
Meanwhile, in a large pan over medium-high heat, add the oil and chicken, cooking about 5-6 minutes until almost cooked through. Stir in prepared curry paste, coconut milk, and broth. Bring to a simmer and cook for 3 minutes. Add the snow peas, reduce the heat to medium-low, and simmer for another 3 minutes. Serve over rice.