Start by rinsing the whole shrimps under cold water to clean them. In a large pot, add the shrimp along with the heads and shells, 1 cup of low sodium chicken broth, and 5 cups of water. Bring this to a gentle boil over medium heat.
Once boiling, add the minced lemongrass, smashed bird's eye chilies, smashed garlic, torn kaffir lime leaves, and sliced galangal. Allow these ingredients to simmer for about 10 minutes, letting the aromas fill your kitchen.
Next, introduce the onion wedges, sliced oyster mushrooms, and tomato wedges into the pot. Stir well and let them cook for another 5-7 minutes until the vegetables are tender.
Stir in the sugar, fish sauce, and lime juice. Taste the broth and adjust the seasoning according to your preference. If you like it spicier, feel free to add more chili paste at this stage.
Pour in the coconut milk and stir gently. Allow the soup to heat through for another 3-5 minutes, but avoid boiling it again to keep the coconut milk from separating.
Ladle the soup into bowls and garnish with fresh coriander leaves. Serve immediately and enjoy the delightful flavors of your homemade Tom Yum Kha Soup with Shrimp.