Matzo Ball Soup
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.