Step 1

Tear dark leafy parts of puntarelle into 2” pieces; set aside. You’ll be left with long white stalks and the core of the puntarelle, which is layered similar to a fennel bulb. Thinly slice core lengthwise (smaller pieces will break away) and set aside.

Step 2

Using your hands, mix egg, pork, breadcrumbs, parsley, 1 leek, and 2 garlic cloves in a medium bowl until well combined; season with salt and pepper. Gently roll heaping teaspoonfuls of mixture into balls, transferring to rimmed baking sheets as you go (you should have about 40 meatballs).

Step 3

Heat ¼ cup oil in a large heavy pot over medium–high. Cook meatballs, turning often to help maintain their round shape, until browned all over, 5–7 minutes. Add remaining leek and 2 garlic cloves to pot and cook, stirring often, until lightly browned and softened, about 5 minutes.

Step 4

Add all but a small handful of reserved sliced puntarelle core to pot and cook, stirring occasionally, until softened, about 4 minutes. Add wine and simmer until liquid is reduced by half, about 2 minutes. Add broth and bring to a simmer. Add all but a small handful of puntarelle leaves to pot. Season with salt and pepper and bring to a boil. Reduce heat and simmer, uncovered, until puntarelle is cooked through and flavors have melded, 25–30 minutes.

Step 5

Toss remaining puntarelle core and greens in a small bowl with lemon juice and remaining 1 Tbsp. oil; season with salt and pepper.

Step 6

Divide soup among bowls and top with dressed puntarelle and Pecorino.

Step 7

Do Ahead: Soup (without dressed puntarelle and Pecorino) can be made 1 day ahead. Dress puntarelle and top soup just before serving.