Prepare all vegetables: slice onions thinly, mince garlic finely, julienne the carrots (cut into thin strips), chop cabbage into bite-sized pieces, and trim the ends of snap peas.
Slice pork belly into thin strips about 2 inches long and ½ inch wide. Clean shrimp by removing heads and shells, then devein.
Heat a large wok or deep pan over medium-high heat (180°C/350°F). Add cooking oil and wait until it shimmers.
Once oil is hot, add minced garlic and sauté until light golden and fragrant, about 30 seconds. Don't let it brown or it will become bitter (mapait).
Add sliced onions to the garlic. Cook until translucent and soft, stirring occasionally, about 2 minutes.
Add the sliced pork belly. Cook while stirring occasionally until the meat starts to brown and render its fat, about 3-4 minutes.
Pour in the soy sauce (toyo) and fish sauce (patis). Stir to coat the meat evenly.
Add chicken broth and bring to a boil. Once boiling, reduce heat to medium-low, cover the pan, and let simmer for 20 minutes or until pork is tender. If liquid reduces too much, add hot water ¼ cup at a time.
Season with ground black pepper to taste. Stir well to combine.
Add shrimp, snap peas, and julienned carrots. Cook for 1 minute, stirring gently.
Add chopped cabbage and cook for another 2 minutes. Vegetables should remain crisp-tender (malutong-presko).
Add the pancit bato noodles. Using two wooden spoons or spatulas, gently toss and mix the noodles with the meat, vegetables, and sauce until well combined.
Continue cooking while stirring occasionally until noodles are tender and have absorbed most of the liquid, about 5-7 minutes. Test a noodle for doneness - it should be soft but still have a slight bite (like al dente pasta).
If noodles are still too firm, add hot broth or water ¼ cup at a time and continue cooking until desired tenderness is reached.
Taste and adjust seasoning with additional fish sauce, soy sauce, or black pepper if needed.
Transfer to a serving plate lined with banana leaves if desired. Serve immediately with calamansi halves on the side.