First, gather all your ingredients and equipment. You'll need a large heavy-bottom pan or wok, and make sure your pork belly is cut into 1-inch cubes.
Heat your pan over medium heat and add oil. Once hot, add the minced garlic and cook until light golden, about 1 minute. Add the chopped onions and cook until they become clear and soft, about 3-4 minutes.
Add the diced tomatoes to the pan. Cook them until they start to break down and become soft, about 4-5 minutes. You can help them along by pressing them gently with your spoon.
Now add your pork belly pieces to the pan. Cook them until they're lightly browned on all sides, about 8-10 minutes, stirring occasionally.
Add the shrimp paste to the browned pork and stir everything together. Let this cook for about 2 minutes to let the flavors combine.
Pour in the vinegar. Don't stir it - just let it boil until most of the liquid has evaporated, about 3-5 minutes. This helps remove the sharp vinegar taste while keeping its flavor.
Pour in the coconut milk and add the chili peppers. Reduce the heat to low - you want a gentle simmer, not a boil. Cover the pan and let it cook slowly for about 40 minutes, stirring occasionally.
After 40 minutes, check if the pork is tender by poking it with a fork - it should be very soft. If it's not tender yet, cook for another 10-15 minutes.
Once the pork is tender, add the sugar and season with salt and pepper to taste. Give everything a good stir and let it cook for another 2-3 minutes.
Your Binagoongan Baboy sa Gata is ready when the sauce is creamy and the pork is fork-tender. Serve it hot over freshly steamed rice.
Remember: Never let the coconut milk boil rapidly as this will make it separate. Keep it at a gentle simmer throughout the cooking process. If the sauce gets too thick while cooking, you can add a little water, one tablespoon at a time.