Warm olive oil in a large pot over medium heat.
Season chicken with a pinch of salt and pepper, then brown in the oil until lightly golden.
Stir in onion, carrots, and celery. Cook until softened and fragrant, about 6 minutes.
Add garlic and tomato paste. Cook, stirring, for 1 minute to caramelize the paste.
Pour in crushed tomatoes and chicken broth. Add potatoes, oregano, red pepper flakes, and remaining salt and pepper.
Bring to a boil, then reduce heat. Simmer gently until potatoes are just tender, about 20 minutes.
Stir in ditalini. Simmer until pasta is al dente, 8 to 10 minutes, stirring occasionally.
Fold in parsley and lemon juice. Taste and adjust seasoning with salt or pepper.
Ladle into bowls and finish with grated Parmesan.