Heat the oil in a pot, then add the onion, celery and carrot. Cook a few minutes, stirring, until the onion is translucent.
Add the chicken broth, potato and pasta.
Bring to a simmer and cook, stirring now and then, until the vegetables are soft and the pasta is cooked through, probably 10-15 minutes.
Taste and season with salt and pepper.
Serve with grated Parmesan at the table.