In a medium bowl, beat the eggs until frothy. Add schmaltz, chicken stock, salt, and pepper, and whisk until emulsified.
Sprinkle matzo meal over wet ingredients and stir gently with a fork until just combined. Do not overmix.
Cover bowl with plastic wrap and refrigerate for at least 1 hour, or up to 24 hours.
While mixture chills, heat oil in a large stockpot over medium heat. Sauté onion for 4-5 minutes until translucent.
Add carrots and celery, cooking for 4-5 minutes until slightly softened. Add garlic and cook for 30 seconds until fragrant.
Pour in chicken stock, add bay leaves, salt, pepper, and shredded chicken if using. Bring to a boil, then reduce to a gentle simmer.
Partially cover and simmer for 30-40 minutes until vegetables are tender.
Meanwhile, bring a large pot of salted water to a rolling boil. Wet your hands with cold water.
Scoop 1 heaping tablespoon of chilled matzo mixture and gently roll into a golf ball-sized ball. Do not pack tightly.
Carefully drop matzo balls into simmering water, cover with a tight-fitting lid, and cook for 30-35 minutes without lifting the lid.
Transfer cooked matzo balls to the simmering soup broth using a slotted spoon.
Remove bay leaves. Stir in fresh dill and parsley. Taste and adjust seasoning with salt and pepper.
Place 2-3 matzo balls in each bowl, ladle hot broth and vegetables over them, and garnish with extra fresh herbs. Serve immediately.