In an electric mixer, whisk the whites until stiff peaks form.
In a separate bowl, beat the egg yolks lightly and mix with the matzo meal, oil, water, salt and pepper. Add this mixture spoon by spoon into the whites, whisking after each addition. Taste and season generously. The mixture should be too sloppy at this stage to form balls. Set aside for 20 minutes, giving it a light fold through after 10 minutes. The mixture should be just solid enough to form balls.
Bring a stockpot or very large saucepan of well-salted water to the boil. With wet hands, and without pressing too firmly, lightly roll the matzo meal mixture into smooth walnut-sized balls and drop into the boiling water. After the last ball has been dropped in, cover and continue to simmer for 30 minutes, covered. Remove the pot from the heat and allow the balls to cool in the water.
Allow the matzo balls to cool in the cooking water in the saucepan. Then store in the fridge in the cooking water until ready to serve. When ready to serve, remove with a slotted spoon and reheat in the chicken soup.
Note: This makes 15-20 or so matzo balls and is a half batch of the original recipe which appears in The Feast Goes On.