In a medium saucepan, bring 3 cups of chicken broth to a gentle boil over medium-high heat. Keep additional broth warm in a separate small pot for adjusting consistency.
Add the pastina to the boiling broth and stir immediately to prevent sticking. Cook for 2-3 minutes less than package directions suggest, stirring frequently. The pasta should be almost al dente as it will continue cooking.
When pastina is tender but still has slight bite, remove the pot from heat. The mixture should be soupy - if it looks too thick, add more warm broth gradually.
Add butter one tablespoon at a time, stirring constantly until each piece is completely melted and incorporated. The mixture should become creamy and glossy.
Add half the Parmesan cheese and stir gently until melted. Add remaining cheese gradually, stirring constantly to create a smooth, creamy texture.
Drizzle with olive oil and season with freshly ground black pepper. Taste and adjust seasoning with salt if needed (the broth and cheese provide most of the salt).
Serve immediately in warmed bowls, garnished with fresh parsley and additional Parmesan if desired. Pass extra warm broth at the table for those who prefer a soupier consistency.
Notes
Storage tip: Keeps in fridge for up to 3 days. Reheat gently on stovetop with additional broth, stirring frequently. The pasta absorbs liquid as it sits, so expect to add moisture when reheating. For best texture, serve immediately after cooking.