Wash leeks thoroughly to remove sand and grit.

Transfer cleaned leeks to a stockpot.

Add carrots, celery, chicken, garlic, ginger, parsley stems, dill stems, peppercorns, salt, and cold water to the pot.

Bring the mixture to a boil over medium heat.

Reduce heat and simmer uncovered for 3 hours, skimming off any foam that rises to the surface.

Prepare the matzo ball mixture by combining matzo meal, parsley, dill, salt, and pepper in a bowl.

Incorporate rendered chicken fat into the matzo meal mixture with your fingers.

Stir in chicken broth and egg yolks to form a stiff mixture.

In a separate bowl, beat egg whites with a pinch of salt until soft peaks form.

Gently fold the beaten egg whites into the matzo mixture, being careful not to deflate them.

Cover and chill the matzo mixture for 30 minutes.

If the matzo mixture is not firm enough after chilling, add more matzo meal.

Remove the chicken from the broth and let it cool slightly.

Shred the chicken meat, discarding the skin and bones.

Remove carrots from the broth and cut into 1/2-inch pieces.

Strain the broth through a sieve lined with dampened paper towels into a clean pot.

Return the strained broth to a simmer.

Form the chilled matzo mixture into roughly 1-inch balls using dampened hands.

Gently drop the matzo balls into the simmering soup.

Simmer the matzo balls, covered, for approximately 45 minutes, or until cooked through.

Test for doneness by cutting one matzo ball in half; it should be uniformly moist inside.

Stir the shredded chicken and carrots into the hot soup to warm through.

Garnish with fresh dill sprigs before serving.