In a medium mixing bowl combine the ground chicken, chicken broth, Parmesan cheese, salt, and pepper. Mix thoroughly until the broth gets absorbed into the chicken, and everything is evenly combined.
Take out four wrappers and cover the rest with a damp dowel. Lay out the four wrappers like ducks in a row. Wet ½ inch of the rim of each wrapper. Scoop a heaping teaspoon of filling into the center of each wrapper, and top with a piece of mozzarella. Fold the wrapper in half like a taco and pinch the edges at the top center. Continue folding the dumpling using your preferred folding method.
At this point, the dumplings can either be cooked immediately, covered and refrigerated for up to a couple hours, or frozen.
To pan-fry the dumplings, use a medium or large nonstick skillet (or cook two batches at the same time using two pans). Heat the skillet over medium-high heat and add 1 ½ tablespoons oil for a medium skillet and 2 tablespoons for a large one. Place the dumplings 1 at a time, sealed edges up, in a winding circle pattern. The dumplings can touch. Medium skillets will generally fit 12 to 14 dumplings, large skillets will fit 16 to 18 dumplings. Fry the dumplings for 1 to 2 minutes until they are golden or light brown on the bottom.
Holding the lid close to the skillet to lessen splatter, use a measuring cup to add water to a depth of roughly ¼ inch (about ⅓ cup water). The water will immediately sputter and boil vigorously, Cover with a lid or aluminum foil, lower the heat to medium, and let the water bubble away for 8 to 10 minutes, until it is mostly gone. When you hear sizzling noises, remove the lid as most of the water is now gone. Let the dumplings fry for another 1 or 2 minutes, or until the bottoms are brown and crisp. Turn off the heat and wait until the sizzling stops before using a spatula to transfer dumplings to a serving plate. Display them with their bottoms facing up so they remain crisp. Serve with hot marinara sauce for dipping.