Combine chicken, pesto, pank, 1/8 tsp. salt, and a pinch of pepper in a bowl and mix with hands until uniform. Using a heaping teaspoon, lightly shape mixture into 3/4 inch round meatballs (about 28 meatballs); place on plate, cover, and refrigerate until needed.
Combine oil, onion, carrot, and celery in a large saucepan, cover, and cook over medium heat until onion is softened, 5 to 7 minutes. Stir in garlic and cook until fragrant, about 30 seconds. Stir in tomatoes with their juice and broth, cover and simmer gently until carrot is softened, 15 to 20 minutes.
Working in batches, process mixture in blender* until very smooth, 1 to 2 minutes. Return pureed mixture to clean pot, cover, and bring to a simmer over medium heat. Stir in pasta and meatballs, cover, and simmer gently until pasta is tender and meatballs are cooked through, 12 to 15 minutes. Season with salt and pepper to taste and serve.
Notes
I used an immersion blender for step 3. I didn't feel like getting the blender out and making a mess with it so the immersion blender is a great alternative.