Prepare the ingredients.
Rinse the oxtail with handfuls of salt, rubbing them to remove some of the oiliness and blood to reduce the gamey smell. Rinse thrice under running water until the water is clear. Drain the water.
Add the washed oxtail to a pan over medium heat. Add all the ingredients for blanching - kaffir lime leaves, ginger and water until the oxtails are fully submerged. Let it blanch for about 10 minutes. Then, switch off the heat and remove the oxtail from the water.
Transfer the oxtail into a pressure cooker, levelling them evenly. Add the lemongrass, half of the kaffir lime leaves, all the cilantro roots, half of the galangal slices, all the spring onion stems, half of the garlic, half of the shallots, half of the chillies, 1/2 tbsp of salt, 1 tbsp of fish sauce, and 1.3L of water. Stir and close the lid of the pressure cooker. Seal it and select the "Tendon" or "Stew" function, or let it cook for 35 minutes.
Heat cooking oil in a saucepan for about 30 seconds over medium heat, or until hot. Add dried chillies and cook until puffed up and lightly browned. Switch off the heat and strain the chillies. Set it aside.
When the pressure cooker is done, carefully release the pressure according to the manufacturer's instructions. Switch off the heat. Open the lid and stir the gravy.
Poke the oxtail with a fork to test for tenderness. The oxtail should be thoroughly cooked by now. If you prefer it to be softer, close the lid and set the pressure cooker to cook for another 15 minutes (or select the "Chicken" function). Once done, release the pressure and check for tenderness again.
Carefully transfer the oxtail, herbs and gravy into another wok over medium heat. Add the rest of the garlic, shallots, birds eye chillies, and galangal. Add 1/4 of kaffir lime leaves, all the tomatoes, 1 tbsp of fish sauce, 1/2 salt, 1.5 tbsp of sugar, and the crispy fried dried chillies. Stir all the herbs until combined. Cover and let it come to a rolling boil, about 8 minutes.
After 8 minutes, taste the gravy and adjust. I added 1 tbsp of fish sauce and 1 tsp of salt, which is optional. Switch off the heat.
Immediately add spring onion leaves, parsley, cilantro leaves and the rest of the kaffir lime leaves. Squeeze 3 limes (or add about 5 tbsp of lime juice), and stir until combined. Taste and adjust as preferred.
Serve with some white rice. Optionally, garnish with some spring onions, parsley and lime juice.