In a large pot, combine the 4 cups of chicken bone broth (or vegetable broth) with the chopped lemongrass and grated ginger. Bring to a gentle simmer over medium heat.
Once the broth is simmering, add the chopped carrots and broccoli florets to the pot. Stir well and let the vegetables cook for about 5-7 minutes, or until they start to soften.
If you’re using the red chili, add it to the pot. Adjust the amount based on your heat preference. Simmer for an additional 2-3 minutes.
Pour in the entire can of full-fat coconut milk, stirring to combine. Allow it to simmer for another 5 minutes.
Remove the pot from heat and stir in the fresh lime juice and sea salt. Taste and adjust seasoning as needed.
Ladle the soup into serving bowls and enjoy warm. Garnish with fresh herbs if desired.