Cut the pork belly into half inch slices. Cut each slice into strips less than half an inch wide.
Place the pork belly in a bowl. Add the soy sauce, rice wine and half of the garlic. Mix well. Cover the bowl and let the pork marinate in the fridge for at least 30 minutes.
Peel the carrot and julienne.
Core and deseed the bell pepper and julienne as well.
Pinch off the tips of the chicharo and pull of the stringy fiber along the sides.
Thinly slice the cabbage.
Peel the shallot and thinly slice.
Heat the wok and pour in a tablespoon of oil.
Stir fry the pork in the hot oil until cooked through. Because the pork had been cut into small pieces and because stir frying requires extremely high heat, the pork should be done in less than five minutes. Scoop them out and transfer to a bowl.
Heat the remaining cooking oil in the wok. Stir fry the carrot, bell pepper, chicharo and cabbage with generous pinches of salt and pepper just until softened, about 15 seconds.
Add the sliced shallot and remaining garlic to the vegetables in the wok and stir fry for another 15 seconds. Scoop out and spread on a plate to cool them to stop the cooking immediately.
In a bowl, mix together all the ingredients for the sauce and pour into the wok. Cook, stirring often, until thickened and no longer cloudy in appearance. Don't worry if it doesn't look too thick. It shouldn't be. Slightly thickened is the ideal texture -- just thick enough to coat the noodles but not make them stick together as they cool.
Taste the sauce. Add salt and pepper, if needed (you may need to if your broth is unseasoned or underseasoned).
Add the noodles to the sauce and toss thoroughly. Cook until heated through.
Throw in the cooked vegetables and quail eggs. Toss well.
Add the cooked pork to the noodles and vegetables. Toss to distribute evenly.
Serve the pancit canton at once.