Heat olive oil in a large pot over medium heat. Add carrots, onion, garlic, celery, salt, and pepper. Cook for 4-5 minutes, stirring occasionally, until vegetables are slightly browned. (Time-saving option: skip this step and add vegetables directly to broth)

Add Parmesan rind and broth to the pot. Cover and turn heat to high until broth reaches a gentle boil. Reduce heat to medium-low and simmer covered for 25-30 minutes, stirring occasionally, until vegetables are very soft and easily pierced with a fork.

Remove Parmesan rind and set aside (discard or save for another use). Use an immersion blender to puree the vegetables until completely smooth. If using a regular blender, carefully transfer hot vegetables in batches (fill no more than halfway), blend until smooth, and return to pot.

Add pastina or small pasta to the simmering soup. Cook for 8-10 minutes, stirring occasionally, until pasta is al dente. (For storing leftovers, cook pasta separately and combine with broth when serving)

Turn off heat. Stir in the juice of one full lemon. Taste and adjust seasonings and lemon juice as desired. Add more broth for a thinner consistency if needed.

Serve soup in bowls and garnish with freshly grated Parmesan, black pepper, a drizzle of olive oil, and chopped parsley if desired.