Warm the oil in a large stockpot over medium heat. Add the garlic, onion, carrots, and celery; season with salt and pepper. Cook until the vegetables start to soften, 4 to 6 minutes. Add the broth and water, bringing it to a rolling boil. Add the chicken breast and 2 sprigs of dill and reduce heat to a very low simmer. Cook 20 to 25 minutes until the chicken is cooked through and no longer pink. Season with salt and pepper to taste.

While the soup is simmering, prepare the matzo ball dough. Place matzo meal, salt, and baking powder in a small bowl and stir well to combine. Place the eggs and oil in a medium bowl and whisk well to combine. Add the matzo meal mixture to the egg mixture and stir until a thick dough forms. Stir in the water until smooth. Refrigerate the dough for 20 to 30 minutes to allow the matzo to thicken further and absorb the moisture.

After the chicken is cooked through, carefully remove the chicken breast and shred it with a fork. Put chicken back in the pot and return the soup to a simmer. Taste the broth and add additional salt if desired.

Once the dough has chilled, form the dough into walnut-sized balls with wet hands. Transfer to a plate. Add all the balls to the soup and increase the heat slightly. Simmer for 15 to 20 minutes, until the matzo balls are cooked through. Garnish with additional dill and serve immediately.