1. In a bowl, whisk together eggs and oil. Stir in matzo meal, salt, and pepper. Whisk in 3 tablespoons of broth. Cover and refrigerate 30 minutes.
2. In a 3 or 4-quart pot, bring 2 quarts of broth to a boil. Form dough into rough 1/2-inch balls and drop into boiling broth. Reduce heat to medium-low, cover pot, and simmer until matzo balls are cooked through and no longer doughy in center, 30 to 40 minutes. Remove with a slotted spoon and use immediately or reserve for up to 4 hours
3. To serve, heat remaining broth and drop in matzo balls and optional chicken. Simmer until heated through, about 5 minutes.