Preheat the oven to 140°C.Trim the beef, then rub with salt and pepper. Place in a heavy-based casserole dish with the stock. Bring to a gentle boil. Cook, covered, in preheated oven for 3 hours or until very tender. Remove the beef with a slotted spoon and set aside.
Skim the cooking liquid and simmer over low heat until the stock has reduced by three-quarters.
Meanwhile, for the garnishes, heat the oil in a shallow frying pan to 160°C. Cook the garlic, eschalots and bitter melon separately, until golden and crisp. Drain on paper towel and set aside.
Place half the butter and the olive oil in a heavy-based frying pan over medium-high heat. When the butter goes frothy and starts to brown, add the garlic and eschalots. Stir for a few seconds, then add the mushrooms and stir-fry for 3 minutes. Remove the pan from the heat. Pour the mushrooms into a sieve placed over a bowl, and then return the strained oil to the pan over medium-high heat. When hot, dust the beef in the Mexican spices and cook until golden all over.
Add the red wine to the pan and simmer until reduced by half. Remove the beef with a slotted spoon and set aside. Add 150ml of the stock to the pan and simmer until reduced by half. Add the bitter melon, carrot and the remaining butter. Reduce the heat to very low. Shake the pan so all the butter is incorporated into the sauce.
To serve, arrange the beef on a plate and top with mushrooms. Spoon over some of the eschalots and garlic it was cooked in. Place a spoonful of the bitter melon and carrot sauce at the base of each piece of beef. Sprinkle the fried onion, garlic and bitter melon chips around the plate. Top each piece of beef with a carrot top and serve immediately.