Step 1
Tie 1 thyme sprig around remaining 3 thyme sprigs; set bundle aside. Season 1 lb. skinless, boneless chicken thighs (about 4), patted dry, all over with kosher salt and freshly ground pepper. Set aside.
Step 2
Heat 2 Tbsp. extra-virgin olive oil in a medium heavy pot over medium. Add 1 medium onion, thinly sliced, and 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt and cook, stirring often, until onion is translucent and softened, 8–10 minutes. Add 3 large carrots, peeled, thinly sliced, 3 celery stalks, thinly sliced, and 3 garlic cloves, thinly sliced, and cook, stirring often, until fragrant, about 3 minutes.
Step 3
Add 1 Parmesan rind (if using), 4 cups low-sodium chicken broth, and reserved thyme bundle. Increase heat to medium-high and bring to a simmer; cook until vegetables are slightly softened, 10–12 minutes. Add reserved chicken; simmer until cooked through and vegetables are completely softened, 10–12 minutes.
Step 4
Meanwhile, cook ½ cup pastina or other small pasta in a small pot of boiling salted water according to package directions; drain.
Step 5
Using tongs, transfer chicken to a plate. Let sit until cool enough to handle, then finely chop. Remove Parmesan rind and thyme; discard. Working in batches if needed, transfer soup to a blender. Add 1 tsp. fresh lemon juice and a generous drizzle of oil; blend until very smooth. Add a little hot water to reach desired consistency if needed. Season with salt and pepper.
Step 6
Transfer soup back to pot; stir in pasta. Ladle soup into bowls. Top with chicken, finely grated Parmesan, and chopped parsley; season with pepper.
