Combine 1 3/4 cups chicken broth, matzo meal, 2 tablespoons minced onion, oil, 1/4 teaspoon salt, yolks, and 1 minced garlic clove, stirring well. Cover and chill 1 hour.
While matzo mixture chills, combine 5 1/4 cups broth, 1/4 teaspoon salt, chopped onion, and next 8 ingredients (chopped onion through drumsticks); bring to a boil. Reduce heat, and simmer 1 hour, skimming surface as needed. Remove chicken; reserve for another use. Strain broth mixture through a colander into a large bowl; discard solids. Return broth to pan; bring to a boil. Reduce heat, and simmer.
Lightly coat hands with cooking spray. Divide matzo mixture evenly into 24 (1 1/2-inch) balls. Gently drop balls into simmering broth. Cover, reduce heat to medium-low, and cook 5 minutes or until done (matzo balls will rise to surface). Remove from heat; stir in dill.