Step 1If the shiitake mushrooms are dried, soak them in cold water for about 2 hours. Squeeze the water out of them and cut them in 1/2-inch pieces.
Step 2Slice the beef into pieces 2 inches long, 1 inch wide and 1/2 inch thick.
Step 3Place the beef strips and mushrooms into a bowl. Add the garlic, soy sauce and sesame oil and mix well. Let marinate for at least 15 minutes.
Step 4Cut the carrot into thirds crosswise so the pieces are about 2 1/2 inches long, then cut each piece lengthwise into thin strips about 1/2 inch thick. The meat and carrot pieces should be about the same size. Soften the carrots by cooking them in a small pot of boiling salted water for about 2 to 3 minutes. Rinse them in cold water and set aside.
Step 5Spear the assorted parts onto toothpicks in this order: green onion, meat, mushroom, carrot, mushroom, meat, green onion. Leave about 1/2 inch on the end of the toothpick so that you can still pick it up comfortably.Repeat until all of the ingredients are used.
Step 6Pour the flour on a plate. In a bowl, whisk together the eggs and add some salt and pepper to taste.
Step 7Add enough oil to a skillet to just cover the bottom. Heat it over medium-low heat.
Step 8Dip the speared ingredients in the flour, making sure that both sides are thoroughly dusted. Next, dip each piece in the egg batter and then carefully place them in the skillet. Cook the pieces on both sides until the beef is thoroughly cooked, 8 to 10 minutes. Taste the first piece and sprinkle with more salt and pepper if needed.