In a saucepan, combine the chicken quarter, onion, carrot, bay leaf, and herbs with enough water to cover. Cook until the chicken is tender and the broth is rich, about 45 minutes. Strain the broth and season with salt and pepper.

Finely chop the remaining onion and garlic, then sauté them in vegetable oil until golden brown. Shred the cooked chicken and mix it with the sautéed onion and garlic; season to taste.

In a mixing bowl, beat an egg with oil and water. Gradually mix in the flour until a smooth dough forms. Cover the dough and let it rest for 15 minutes to develop ease in handling.

Roll out the dough to about 1/8 inch thick. Cut it into 2-inch squares. Place a teaspoon of filling in the center of each square, fold over, and seal the edges securely to create little pockets of goodness.

Bring the prepared broth to a boil and gently add the dumplings. Cook until they float to the surface, which signals they’re fully cooked—about 5-7 minutes. Serve hot in broth, garnished with chopped herbs.