Purée the green onions and eggs together in a food processor fitted with the metal blade until they are smooth and fluffy. Add the potatoes and pulse until the mixture is finely chopped but still retains some texture. Add the salt, pepper and matzo meal and quickly process to combine. Do not overprocess. Pour the batter into a mixing bowl.
Let the batter sit for 15 minutes, covered with plastic wrap to prevent discoloration.
Heat 3/4 inch of oil in a large nonstick skillet on medium high heat. Pour a tablespoon of batter into the skillet to test the oil. If it is hot enough, the pancake will begin to sizzle and brown. Taste the pancake and check the seasoning.
Spoon tablespoons of the batter into the skillet, making sure that there's a little room between each pancake. Flatten them with the back of a spoon and use a spatula to round out the sides, if necessary. Fry the pancakes until they are golden brown on one side, about 2-3 minutes, then turn them and brown the other side, about 2 more minutes. They should be golden brown.