Drain the soaked mung beans and add them to a high-speed blender or food processor with 3/4 cup (960 ml) of water.
Blend until you have a smooth, thick batter, adding more water one tablespoon at a time if necessary to reach the right consistency.
Pour the batter into a large mixing bowl.
Stir in the eggs, minced garlic, fresh chile, chopped scallions, and grated carrot.
Season generously with salt and freshly ground black pepper and mix until everything is well combined.
Heat a large skillet or non-stick pan over medium-high heat.
Add enough oil to coat the bottom of the pan.
Once the oil is shimmering, reduce the heat to medium.
Ladle the batter into the pan to form your desired pancake size—you can make several small ones or one large one.
Cook for about 5 minutes, or until the bottom is golden brown and crispy.
Carefully flip the pancake(s) and cook for another 5 minutes on the other side until cooked through and golden.
Repeat with the remaining batter, adding more oil to the pan as needed.
Transfer the cooked pancakes to a wire rack or a plate lined with paper towels to drain any excess oil.
Serve hot, whole or cut into wedges, with your favorite dipping sauce.