Cut the pork shoulder into uniform 1-inch cubes and place in a bowl. Do the same with the pork liver (atay), but keep it separate. Soak the liver in milk for 30 minutes to remove any bitter taste (ibabad ang atay sa gatas para maalis ang pait).
While the liver is soaking, prepare your vegetables. Peel and cut the potatoes (patatas) and carrots into cubes slightly smaller than the meat. Dice the red and green bell peppers (siling pangsigang) into ¾-inch squares. Finely chop the onion (sibuyas) and mince the garlic (bawang). Dice the tomatoes (kamatis) into small pieces.
Heat your thick-bottomed pot (kaldero) over medium heat (katamtamang init, 350°F/175°C). Add cooking oil (mantika) and annatto seeds (atsuete). Stir until the oil turns orange, then remove and discard the seeds using your slotted spoon (sandok na may butas).
In the orange-tinted oil, sauté the chopped onions until they become translucent (malinaw), about 2-3 minutes. Add the minced garlic and cook until fragrant (mabango), about 1 minute. Add the diced tomatoes and cook until they start to soften and release their juices, about 5 minutes.
Add the cubed pork to the pot and cook until the meat browns on all sides (lutuin hanggang maging kulay kayumanggi), approximately 5-7 minutes. Pour in the fish sauce (patis) and stir to combine. Add water (tubig) and bay leaves (dahon ng laurel). Bring to a boil, then reduce heat to low (300°F/150°C). Cover and simmer for 30-35 minutes or until the pork becomes tender (malambot).
Once the pork is tender, add the cubed potatoes and carrots. Cook for 5 minutes at medium-low heat (325°F/165°C). Add the bell peppers and drained garbanzo beans (garbanzos). Drain the liver from the milk, pat it dry, and add it to the pot along with the raisins (pasas).
Cook for another 5-7 minutes until the liver is just cooked through (lutong-luto) but still tender, and the vegetables are crisp-tender (malutong-malambot). The potatoes should be easily pierced with a fork but still holding their shape. Taste and season with salt (asin) and pepper (paminta) as needed.
If the sauce is too thin (manipis), remove the lid and let it simmer until it reaches your desired thickness (kapal). The final sauce should be thick enough to coat the back of a spoon. Remember that the sauce will continue to thicken as it cools.
Let the menudo rest for 5-10 minutes before serving (palamiginin ng kaunti bago ihain). This allows the flavors to settle and the sauce to thicken slightly. Serve hot over steamed white rice (mainit na kanin).
For leftovers (tira), let the menudo cool completely before transferring to an airtight container. When reheating (pag-iinit), warm gently over low heat (mababang init, 165°F/75°C), adding a small amount of water if needed to maintain the sauce consistency. Stir occasionally to ensure even heating.
Note: Like many Filipino stews, menudo often tastes better the next day (mas masarap kinabukasan) when the flavors have had time to develop fully. If making ahead, you can cook it up to a day in advance and reheat gently before serving.