To make the matzo balls: Whisk together the eggs, oil, and seltzer in a large bowl. Add the matzo meal, 1/2 teaspoon salt and 1/4 teaspoon pepper. Stir the egg mixture into the matzo just to combine; cover the bowl with plastic wrap and refrigerate until firm, at least 30 minutes and up to 4 hours.
To make the soup: Heat the oil in a large pot or Dutch oven over medium-high heat. Add the garlic, onion, and half the chopped carrots and cook, stirring, until the vegetables begin to soften, 5 to 7 minutes. Add the chicken, broth, water, peppercorns and 3/4 teaspoon salt and bring to a boil. Simmer until the chicken is cooked through, 10 to 12 minutes. Transfer the chicken to a plate; let cool. Shred the chicken with 2 forks and reserve for the soup.
Strain the broth through a fine mesh sieve into a large bowl and return to the pot. Add the remaining carrots and bring to a simmer. Cook until the carrots are just tender, about 5 minutes. Stir in the reserved chicken and heat until warmed through.
Bring a large pot of salted water to a boil. Scoop the matzo mixture into 8 small balls (about a 1 1/2 inches each). Gently add the matzo balls and simmer, covered, until the balls are fluffy and soft, 40 to 45 minutes. Add two matzo balls to each bowl and ladle the hot soup overtop. Serve sprinkled with dill and additional black pepper.
The balls came out okay, but the soup itself was bland. I've had better. Won't make this one again.