Cook coriander, cumin, and white peppercorns in a small skillet over medium, stirring constantly, until toasted and fragrant, 2 to 3 minutes. Transfer mixture to a small heatproof bowl, and let cool completely, 5 to 10 minutes. Finely grind mixture using a spice grinder or mortar and pestle. Set aside.

Place shallots, cilantro, water, galangal, lemongrass, basil, chiles, garlic, lime zest, shrimp paste, salt, and ground coriander mixture in a food processor. Process until mixture becomes a thick, slightly chunky paste, about 4 minutes, stopping to scrape down sides as needed. (If the mixture is too thick to blend well, add more water, 1 teaspoon at a time.) Transfer to an airtight container, and store in refrigerator up to 2 weeks.

Heat oil in a large wok or Dutch oven over medium-high until shimmering. Add lime leaves and ½ cup Green Curry Paste; cook, stirring constantly, until fragrant and softened slightly, about 2 minutes. Stir in coconut milk, fish sauce, and sugar. Bring to a simmer over medium-high, stirring occasionally. Stir in chicken, zucchini, and bell pepper; reduce heat to medium to maintain a gentle simmer. Simmer, covered, stirring once or twice, until chicken is cooked through (chicken will be firmer and will no longer be pink) and vegetables are tender, 6 to 10 minutes.

Remove from heat; stir in basil until wilted. Season to taste with salt, and garnish with additional basil. Serve over rice.