Prep your produce: Slice the leek and rinse well to remove grit. Dice the celery, carrot, and zucchini. Cut asparagus into 1-inch pieces.
Mince the garlic. Rinse and drain the beans.
Sweat the aromatics: Warm 2 tablespoons olive oil in a large pot over medium heat. Add leek, celery, and carrot with a pinch of salt.
Cook 5–7 minutes, stirring, until soft and glossy, not browned.
Build flavor: Stir in garlic and a pinch of red pepper flakes. Cook 30 seconds until fragrant. If using, pour in the white wine and simmer 1–2 minutes to reduce slightly, scraping the pot.
Add broth and optional rind: Pour in 6 cups broth and add the Parmesan rind if you have one.
Bring to a gentle boil.
Cook the pasta: Add the small pasta and cook until just shy of al dente, 1–2 minutes less than package directions. Keep the soup at a lively simmer, not a rolling boil.
Add beans and tender veg: Stir in cannellini beans, zucchini, and asparagus. Simmer 3–4 minutes until the asparagus is bright and just tender.
Finish with greens: Add peas and baby spinach.
Cook 1–2 minutes until the greens wilt and peas are warm.
Season and brighten: Remove the Parmesan rind. Add lemon zest and a squeeze of juice. Taste and season with salt and pepper.
The broth should taste savory and lively.
Swirl in pesto: Off the heat, stir 2–3 tablespoons pesto into the pot for a subtle herbal note, or spoon pesto into bowls and ladle the soup over it for a more pronounced hit. Either way, don’t boil after adding pesto.
Serve: Ladle into warm bowls. Top with extra pesto, chopped herbs, a drizzle of olive oil, and grated Parmesan if you like.
Add more lemon at the table.