Rehydrate potatoes by soaking them in a bowl of cold water to soften then drain in a colander. Wrap potatoes in paper towels and squeeze out excess moisture. Add the carrots, zucchini, onion and matzoh meal to the potatoes.
Whip eggs with a whisk, until frothy. Add the egg mixture, a little at a time, to the potatoes until mixture is bound. Potato and vegetable mixture should be firm (versus runny). Season with salt and pepper.
In small skillet, heat the vegetable oil over medium high heat. Place rounded teaspoons of potato mixture into pan and fry on both sides until golden brown.