In a mixing bowl, whisk together the eggs, vegetable oil, water or chicken broth, salt, and black pepper until well blended.
Gradually mix in the matzo meal until combined. If using, fold in the chopped dill or parsley. Refrigerate the mixture for at least 30 minutes to firm up.
In a large soup pot, heat the chicken broth over medium heat. Add the diced carrots, celery, onion, garlic, and dried thyme. Season with additional salt and black pepper to taste. Bring to a simmer.
While the soup is simmering, wet your hands or a spoon with water and form the matzo mixture into small balls, about the size of a walnut.
Once the broth is simmering, gently drop the matzo balls into the pot. Cover and cook for 20-25 minutes, until the matzo balls are cooked through and fluffy.
Once the matzo balls are done, remove the pot from heat and let it sit for a few minutes. Serve hot, garnished with additional fresh dill or parsley if desired.