Begin by finely chopping the shrimp or pulse it in a food processor until you achieve a coarsely minced texture. In a mixing bowl, combine the shrimp with chopped broccoli, grated carrots, minced garlic, grated ginger, soy sauce, sesame oil, and cornstarch. Mix thoroughly until the filling becomes sticky, which should take about 2-3 minutes.

Take a wonton wrapper and place it in the palm of your hand. Spoon approximately 1 teaspoon of the shrimp filling into the center of the wrapper. Lightly wet the edges of the wrapper with water to help seal it. Carefully fold the wrapper over the filling to create a half-moon shape, then pinch and pleat the edges to ensure a tight seal.

Prepare your steamer by lining the basket with parchment paper or cabbage leaves to prevent sticking. Arrange the shrimp dumplings in a single layer, ensuring they are spaced apart. Bring water to a simmer and place the steamer on top. Steam the dumplings for 6-8 minutes, or until the wrappers turn translucent and the filling is cooked through.

Once the shrimp dumplings are perfectly steamed, carefully remove them from the steamer and let them cool for a moment. Serve warm with a homemade dipping sauce made from soy sauce, rice vinegar, sesame oil, and chili flakes.