In a medium bowl, combine pork, minced shrimp, cornstarch, salt, pepper, ginger, and carrot.
Place wonton wrappers on work surface and cover with a damp cloth. Fill a small bowl with water. Line a baking sheet with parchment. Put 1 wonton wrapper on the work surface with an edge pointed towards you. Add 1 teaspoon of filling right below the center of the wrapper. Tuck the corner nearest you over the filling to cover it. Tightly roll up into the bottom is even with the side corners, creating a triangle. Dip your finger in the water and wet the left and right corners. Fold each corner over the filling. Place on prepared baking sheet and cover with a moist towel. Repeat until you run out of wrappers or filling.
In a large pot, drizzle oil over medium high heat. Cook the onions until beginning to soften and become translucent, 3-5 minutes. Stir in garlic and cook until just beginning to turn golden. Add in the chicken broth. Scrape the bottom of the pot to remove any browned pieces created from the onions and garlic. Season with fish sauce and black pepper, then increase the heat to high. Once boiling, carefully add 24 of the dumplings to the pot, cover, and reduce heat to medium. Simmer until the filling has cooked through, 10-15 minutes. Season with more fish sauce and black pepper if desired. Top with green onions and serve immediately.