Prepare Base Flavors: In a deep pot, heat oil and sauté garlic, onions, and ginger until fragrant and onions are translucent.
Brown Meat: Add beef brisket and brown on all sides. Once browned, add the beef tendons.
Initial Simmer: Add enough water to cover the meat pieces. Bring to a boil, then reduce heat and simmer for 45 minutes.
Create Clear Broth: Turn off the heat and strain the soup through a fine-mesh sieve to create a clear broth. Set aside the meat pieces.
Tenderize Tendons: Return the clear broth and tendons to a clean pot (set aside the beef). Bring to a boil and simmer until tendons are soft (90-120 minutes), adding water as needed.
Add Remaining Ingredients: Return the beef to the pot and add tripe, finger chilies, and bile (if using). If using bitter gourd, place it in a muslin cloth together with tamarind or kamias, wrap it well, and add to the pot. Simmer for 30 minutes.
Extract Flavors: If using the muslin cloth method, press it against the side of the pot to extract the juices into the soup.
Season: Add fish sauce or salt to taste. If adding spinach, stir it in just before serving until wilted.
Serve: Ladle into bowls and serve hot.