Grate the carrot and add it to a food processor along with the chicken mince, garlic cloves, minced ginger, green onion, sesame oil, and soy sauce. Pulse until everything is finely chopped.
Heat up a frying pan over medium-high heat and fry the mixture in some sesame oil until golden brown.
Place a tbsp filling in the middle of a dumpling wrapper and wrap it into the shape you like.
Heat up the skillet again and fry your dumplings on one side until crispy, then turn over and repeat. Pour the water into the pan and cover with a lid. Let the dumplings steam until all the water is absorbed.
Finely chop garlic and green onion. Add garlic, green onion, red chili flakes, and sesame seeds to a bowl. Pour the hot oil into the bowl.