Step 1 Bring 1 cup lightly salted water to boil in small saucepan. Add carrot and parsnip, and simmer until vegetables are very tender, 12 to 15 minutes. Drain, reserving cooking water, and transfer vegetables to food processor. Place matzo meal in small bowl and stir in 1/3 cup reserved cooking water. Let sit so matzo meal can soften as it soaks in liquid, 5 minutes.
Step 2 Heat oil in 8-inch skillet over medium heat. Add onions, sprinkle them lightly with salt and pepper, and saute, stirring, until soft, shiny and just beginning to color palest gold, 8 to 9 minutes. Don't let them brown. Transfer onions and any remaining oil to food processor. Add shallots and dill to food processor and puree until fairly smooth. Transfer mixture to large wooden chopping bowl or wooden chopping board. (Don't wash out food processor if you are grinding your own fish.)
Step 3If your fish is not ground, put it, about 2 teaspoons salt and 1/8 teaspoon pepper in bowl of food processor and pulse just until mixture is chopped fine, but not pasty. Add fish to wooden bowl or board. (If you are using pre-ground fish, add it now, seasoned with salt and pepper.) Add soaked and softened matzo meal mixture. Beat eggs and yolks in bowl until thick and lemon-colored. Using hand chopper or cleaver, work beaten eggs and lemon juice into fish mixture, a little at a time. (Hand-chopping at this point incorporates air into mixture, making it lighter and fluffier than pulsing in food processor.)
Step 4Poach 1 teaspoon fish mixture in lightly salted boiling water for a few minutes. Taste and, if needed, add salt and pepper. Chill fish mixture, covered, 1 to 4 hours. It will be easier to mold and fish balls will cook fluffier.