Prepare all your ingredients: slice chicken, thinly slice shallots, mince garlic, slice galangal, bruise lemongrass stalks, and tear kaffir lime leaves. Slice mushrooms and halve cherry tomatoes.

Heat coconut oil in a large pot or Dutch oven over medium heat. Add shallots and cook for 2-3 minutes until softened. Add minced garlic, sliced galangal, bruised lemongrass, and kaffir lime leaves. Sauté for another 2 minutes until fragrant.

Add the chicken pieces to the pot and cook for 3-5 minutes, stirring occasionally, until lightly browned on all sides. It doesn't need to be cooked through at this stage.

Pour in the chicken broth and one can of coconut milk. Bring the mixture to a gentle simmer. Once simmering, reduce the heat to low, cover, and let it cook for 10-12 minutes, allowing the flavors to meld and the chicken to cook through.

Remove the lid and stir in the remaining can of coconut milk and the red curry paste. Whisk well to ensure the curry paste is fully dissolved. Add the fish sauce, fresh lime juice, and brown sugar. Taste and adjust seasonings if necessary; you might want more lime for tang, more fish sauce for saltiness, or more sugar to balance.

Add the sliced mushrooms and halved cherry tomatoes to the soup. Continue to simmer for another 3-5 minutes, or until the vegetables are tender-crisp.

Before serving, remove the lemongrass stalks, galangal slices, and kaffir lime leaves from the soup (they are not meant to be eaten). Ladle the hot soup into bowls. Garnish generously with fresh chopped cilantro and optional sliced red chili for an extra kick.