Heat the oil in a dutch oven over medium-high heat. Add the onion, celery, carrot, and crushed red pepper to the hot oil and cook, stirring often, until vegetables are softened, about 5 minutes.
Add the potatoes, garlic, parsley, rosemary, ½ tsp salt, and ¼ tsp freshly ground pepper to the pot and stir to combine. Pour in the chicken stock and bring to a boil. Place a lid on the pot and reduce the heat to medium-low. simmer, covered, until potatoes just start to become tender, about 10 minutes.
Add the pasta to the pot and stir to combine, if the pasta isnt covered in liquid add a little water. Return to a boil then reduce heat to medium-low. Place the lid back on the dutch oven and simmer, stirring occasionally, until the pasta is cooked, 10 to 15 more minutes. Season with salt & pepper to taste.
Ladle into bowls and top with freshly grated Parmesan.
