In a large pot, heat olive oil and butter over medium heat until melted and shimmering. Add chopped onion, diced carrots, and chopped celery, and sauté for 5-7 minutes until the vegetables are softened and fragrant.

Stir in minced garlic and sauté for 1 minute until fragrant. Then, add in diced chicken, seasoning with salt and pepper, and cook for 3-4 minutes until the chicken pieces begin to brown.

Pour chicken broth into the pot, then increase heat to medium-high until boiling. Reduce heat to low, cover, and let it simmer for 15-20 minutes.

Stir in ditalini pasta and let it cook uncovered for 8-10 minutes, or until the pasta is tender.

Reduce heat to low and stir in heavy cream. Simmer gently for an additional 3-5 minutes.

Stir in grated Parmesan cheese until melted, adjusting the seasoning with more salt and pepper if needed. Serve hot, garnished with fresh parsley or basil.