Begin by combining all of your sauce ingredients in a mixing bowl. Give everything a good whisk until it's evenly combined, then set the sauce aside.
Slice the chicken into thin, evenly sized strips.
Shred the carrots, dice the onion, cut the green beans if they're too long, and slice up the cabbage.
Heat a large wok over medium-high heat and add a little cooking oil.
Add the sliced chicken and season it with salt and pepper, then stir-fry until it's cooked through.
Once the chicken is fully cooked, remove it from the wok and transfer it to a mixing bowl.
Now add a little more oil if necessary, and add the shrimp.
Cook the shrimp until they're pink, opaque, and cooked through. Then remove them from the wok and add them to the bowl with the chicken.
Add the green beans, onions, and carrots to the wok. Sauté everything until the vegetables begin to soften and the onions start turning translucent.
Once the onions have softened, stir in the fresh minced garlic and Continue cooking just until the garlic becomes fragrant.
Add the cabbage in batches, stirring each batch into the vegetables already in the wok.
As the cabbage cooks, it'll begin to soften and shrink down, making room for more. Continue adding the cabbage until everything has been incorporated.
Once all the vegetables are cooked to your liking, transfer them to a large mixing bowl and set them aside.
Pour the sauce we prepared earlier directly into the wok and bring it to a boil.
Begin adding the dry Pancit Bihon noodles and use a pair of small tongs to gently move the noodles around, separating them as they begin to soften.
Continue gently stirring and separating the noodles until they're tender and have absorbed most of the sauce.
Add the cooked chicken and shrimp back into the wok.
Gently stir them into the noodles until they're evenly distributed and then start adding the cooked vegetables in batches.
Continue working in batches until all the cabbage, carrots, green beans, and onions are evenly incorporated.
Once everything is combined and heated through, turn off the heat and serve with fresh lime wedges.