Kreplach (Chicken and Liver Dumplings)

Ingredients

• 6 tablespoons canola oil
• 1 small chicken breast (about 5 ounces; ½ cup chopped), cut into ½-inch pieces
• 3 chicken livers (about 3 ounces; ¼ cup chopped), cut into ½-inch pieces
• ½ teaspoon kosher salt, plus more to taste
• 3 medium onions, roughly chopped
• 1 egg, lightly beaten, divided
• ½ teaspoon freshly ground black pepper
• 3½ cups all-purpose flour, sifted
• 1 tablespoon salt
• 1 egg, lightly beaten
• 1 cup lukewarm water
• Canola oil, for drizzling
• Chicken soup
• Fried onions