This is a kind of classic Korean meat patty that is also known as donggurang ddeng (동그랑땡). Though some people make this with just beef and sometimes tofu, I like to skip the tofu and add pork instead. You can dip the patties in a little soy sauce and vinegar if you like.
4 brown mushroom (shiitake)
1 medium onion
10 oz ground pork
10 oz lean ground beef
1 tbsp crushed garlic
1 tsp grated ginger
1 tbsp green onion
1/2 cup flour
5-6 tbsp of vegetable oil
salt and pepper to taste
Mix ground beef and pork, put dash salt and pepper – set aside.
Discard the ends of shiitake mushroom stems and slice caps into small pieces. Chop onions and grate carrots.
Mix the ground beef and pork together with the sliced vegetables. Add garlic, ginger, and green onion.
Add about 3 tbsp of the flour into the mixture and begin kneading. Add more flour if necessary. Form small, flattened round patties with your hands, about 1½" diameter. Set aside.
Beat eggs well and add a dash of salt and pepper. Set aside in a bowl. Add the rest of the flour to a plate.
Prepare the patties for frying: dip each patty into the flour plate, coating lightly. Then dip the flour coated patties into the egg mixture.
Heat enough vegetable oil to cover a frying pan and fry the patties on medium heat for 3-4 min on each side.