In a large bowl, beat the eggs and the oil with a fork until slightly puffy. Add water and matzo meal, and mix.
Add salt, pepper, baking powder, and *optional* mashed vegetables. The mixture should be neither hard nor liquid. If too hard, add more water.
Cover with plastic wrap and place in the refrigerator for about 20 to 30 minutes.
After the matzo ball mix has been set, with wet or greased hands, create ping pong size balls. The mixture is going to be a little sticky, and that's OK.
Bring a large pot of water with a spoon of salt, or your soup to a brisk boil. Reduce heat to a simmer and drop the matzo balls gently into the liquid.
Cover the pot with a lid and simmer for 20-30 minutes. The balls should be floating on the surface and look soft and airy. Of course, you can cook them for longer, but I find that the best texture is around the 20 minutes mark.
Using a slotted spoon, remove the matzo balls from the water and place them on a plate or a tray.