Put the shredded zucchini in the colander and sprinkle with the salt. Set the colander in the bowl.
Using your hand, press down on the zucchini so that as much liquid as possible drains out into the bowl. Stir the zucchini and repeat. Throw away the liquid.
Put the zucchini in the bowl and add the eggs, flour, cheese, and scallions. Mix well.
Put the skillet on the stove and turn the heat to medium. When the skillet is hot (flick some water on — it should dance and evaporate immediately), add the oil.
Using the tablespoon, scoop blobs of the zucchini mixture from the bowl and spread it into a round, flat nest on the skillet: it should make a circle that's about 2 inches wide and 1/4 inch thick. Repeat to fill the skillet.
Cook until the bottoms are deeply golden, about 5 minutes, then turn the pancakes over and cook 5 more minutes. Repeat with the remaining mixture.