Preparation

Make the broth:

• Put the carrots, leek tops, onion, fennel, celery, garlic, bay leaf, thyme, and parsley in a 4-qt. (or larger) saucepan. Add 10 cups cold water and bring to a simmer over medium-high heat. Reduce the heat to medium low and simmer for 1 hour. Strain the broth into a heatproof bowl and discard the solids. Measure out 5 cups of broth for use in the soup; save the remaining broth for another use. Rinse and dry the saucepan and return it to the stove.

Finish the soup:

• In the saucepan, heat the olive oil over medium-low heat. Add the shallots, leeks, garlic, and a generous pinch of salt. Cook, stirring occasionally, until the vegetables are softened but not browned, about 5 minutes. Stir in the carrots and sugar. Cover, reduce the heat to low, and cook, stirring occasionally, until the carrots are soft, 15 to 20 minutes.

  Add the 5 cups broth and the carrot juice. Bring to a simmer, uncovered, over medium-high heat. Reduce the heat to low and simmer gently for 10 minutes.

  Wrap the ginger in a small square of cheesecloth and use the cloth to squeeze the ginger juice into the soup (discard the squeezed-dry ginger). Remove the pan from the heat.

  Working in batches, purée the soup in a blender until smooth. Pour each batch of the puréed soup into a medium-mesh sieve set over a clean heatproof container. Use a rubber spatula to help the soup pass through, but don’t press on the solids yet. Once the last batch has drained through the sieve, press lightly on the solids (but don’t mash them through the sieve) to extract the remaining liquid. Discard the solids. Season to taste with salt, pepper, and 1 to 2 tsp. of the lemon juice.

  When ready to serve, peel and core the apple and cut it into medium dice. In a small bowl, toss the apple with 2 tsp. of the remaining lemon juice. Reheat the soup, if necessary, and ladle it into individual serving bowls or cups. Serve immediately, garnishing each bowl with a small spoonful of the diced apple.