Bring all ingredients to a boil in an 8- to 10-quart heavy pot. Skim froth. Reduce heat and gently simmer, uncovered for 3 hours.
Pour stock through a fine-mesh sieve into a large bowl and discard solids. If using stock right away, skim off and discard any fat. If not, cool stock completely, uncovered, before skimming fat, then chill, covered. Reserve a few tablespoons of the skimmed fat (schmaltz) if you wish to use them in matzo balls (below).
Stock can be chilled 3 days in the refrigerator or frozen 1 month.
There are two matzo ball camps: those that like them heavy and leaden at the bottom of a bowl and those that like them light and fluffy–these are the latter, and in my mind, the better ones.
If you can’t find matzo meal, pulse a few pieces of matzo in your food processor until it is a coarse powder. If you can’t find matzo, well, you obviously do not live in New York City.
3Mix all matzo ball ingredients in a bowl. Cover and place in the refrigerator for 30 minutes.
Bring 1 1/2 quarts of well-salted water to a brisk boil in a medium sized pot.
Reduce the flame. Run your hands under water so they are thoroughly wet. Form matzo balls by dropping spoonfuls of matzo ball batter approximately 1-inch in diameter into the palm of your wet hands and rolling them loosely into balls. Drop them into the simmering salt water one at a time. Cover the pot and cook them for 30 to 40 minutes.
About ten minutes before the matzo balls are ready, bring prepared chicken stock to a simmer with the sliced carrot in it. Ladle some soup and a couple matzo balls into each bowl and top with a couple snips of dill. Eat immediately.