Heat 2 tsp of the vegetable oil in a large, deep saucepan over medium-high heat. Cook the pork ribs for 4 minutes, turning until browned on both sides. Transfer to a plate once cooked. Add another 2 tsp of oil to the pan and cook the pork belly for 4 minutes, turning until browned. Set the ribs aside.
Add the remaining vegetable oil to the pan and heat over medium heat. Add the onion and cook for 2 minutes, stirring and scraping any bits from the base of the pan. Add the tomato and capsicum and cook for a further 4 minutes or until they start softening, stirring occasionally. Return the pork to the pan with 1.5 liters (51 fl oz/6 cups) water. Bring to a boil, then reduce the heat to low–medium and cook for 15 minutes.
Meanwhile, place the tamarind pulp in a heatproof bowl and cover with the boiling water. Leave to stand for 15 minutes to soften, then mash to combine well (I use my hands). Strain through a sieve into a bowl, pushing the seeds to extract their liquid. Discard the solids.
Add the tamarind mixture to the pan and cook for 5 minutes. Add the horseradish and eggplant, and cook for 5 minutes, or until the eggplant is almost tender. Add the beans and cook for a further 3 minutes, or until the vegetables and meat are tender. Add the salt and season with freshly cracked black pepper; the soup should be a balance of sour and salty. Transfer to a large serving bowl and scatter with spring onions. Serve with steamed rice, fish sauce, and calamansi.