Red curry is a two step process, but fortunately both steps are rather easy. Step 1, make the curry paste.
In a food processor, combine lemongrass, red chiles, ginger, garlic, lime zest and salt. Apply a long pulse or blend a few times to mix the ingredients. After a rough paste is achieved, add 1/4 cup coconut milk and blend 1-2 minutes, scraping the sides about every 30 seconds, until a smooth paste is achieved. Now on to step 2, making the red curry.
Add the red curry paste to a deep sauté pan or pot over medium-low heat. Stir in the remaining coconut milk. Add carrots, and let cook for about 7-10 minutes. After 7-10 minutes, gently stir in straw mushrooms and baby corn and wait another 3-5 minutes. Finally, add water chestnuts and soy sauce to taste, and cook for 2 more minutes. Serve piping hot with prepared rice.