Place everything in a large stock pot and bring to a boil over high heat.  Reduce to simmer and cook covered for about 45 minutes to 1 hour.  Strain and add back the carrot slices.

For the matzo balls:

Beat eggs lightly with cold water.  Add the chicken fat and stir until the fat dissolves.  Add salt and pinch or two of white pepper.  Gradually beat in the matzo meal, a couple of tablespoons at a time,  proceeding slowly as it thickens so you don’t add too much.  The mixture should be about as thick as light mashed potatoes, and a little soft and spongy.  Chill covered for 5-7 hours.  Half an hour before serving time make matzo balls.  With wet hands shape  the mixture into balls about 1 inch in diameter.  Drop gently into boiling chicken soup.  Cover the pot loosely and let boil at a moderately brisk pace for about 25 minutes.