Mince onion, carrot, mushroom, leek (or green onion) super finely with a knife or use a mini food chopper. Leeks (or green onion), however, won't mince very well in a food chopper, so I recommend mincing them with a knife as finely as you can. You will need to collect 1/4 cup of each minced vegetable and mushroom. Set them aside.
Place tofu in a fine kitchen cloth and twist it to squeeze the water out. Unfold the cloth and crumble the tofu.
Mix ground meat, tofu, minced vegetables, mushroom, garlic, ginger, oyster sauce, egg, salt, pepper, and 1 egg in a mixing bowl. Knead the mixture for 2-3 minutes. Form them into meatballs using a small cookie scoop (1 1/2 tbsp). It will make about 3 dozen meatballs.
Put flour in one shallow bowl (I used a pie dish) and the remaining eggs in another; beat the eggs. Flatten each meatball a little to make a disk shape. Coat them lightly with flour, followed by beaten eggs.
Heat 1 tablespoon of oil in a skillet over medium low heat. Add a few patties (without crowding the skillet too much) and cook until golden brown, about 3-4 minutes. Flip to the other side and cook another 3 minutes or until fully cooked. Adjust the heat to low if the patties brown too quickly.
After the first batch has been pan-fried, wipe the skillet with a paper towel to remove any residue in the skillet. This will help the next batch look clean, without burnt pieces sticking on the surface. Start pan-frying the second batch and repeat the steps.
Serve meat tofu patties warm or at room temperature with a dipping sauce.
To make the dipping sauce, mix soy sauce, vinegar, and sugar in a small mixing bowl.
* Storage Tips: Store leftover meat tofu patties in the refrigerator for up to 1 week. They also freeze beautifully. Just put them in a zipper bag and freeze them up to 3 months. To reheat, thaw the patties first and fry them again in a bare skillet (no oil needed) over medium-low heat, or microwave them until hot.