Peel the potatoes and cut them into pieces roughly the same size as the pasta.
Slice each potato in half, cut it into three long strips, then slice horizontally to create small cubes.
Keep the skin on the carrot and cut it along with the celery.
Then chop the onion and garlic, setting everything aside. These will be blended later to make our creamy base.
Break the fusilli in half (if using) so it matches the size of the ditalini, this will help everything cook evenly.
Cut the provolone in half, then into cubes, using as much or as little as you like. You can save half for another pasta or throw it all in for a super creamy texture.
Add the celery, carrot, onion and garlic to a blender along with 3 tablespoons of EVOO and a small splash of water. Blend until smooth and creamy.
Place a deep pot over medium low heat and add 4-6 tablespoons of EVOO.
Add the rosemary leaves to the pot and toast them for one to two minutes until fragrant.
Pour in the blended soffritto.
Add a splash of water, raise the heat to medium and mix well.
Add the diced potatoes and cook for 7 to 10 minutes. If the mixture starts to dry out, add another splash of water, keeping an eye on it to prevent sticking.
Pour in enough vegetable stock to fully cover the potatoes, then mix, cover with a lid and simmer for 10 to 20 minutes.
After 10 minutes, check a piece of potato. If it still feels undercooked, continue cooking, stirring the bottom of the pot gently to prevent sticking and mash a few potatoes lightly to help thicken the sauce.
Add the pasta to the pot and pour in the remaining vegetable stock (making sure the stock is hot) until all the pasta is covered. If you run out of stock, add boiling water and avoid adding cold liquid because it will stop the cooking process.
For the next 10 minutes, keep stirring and watching the pot. Taste and adjust with salt and pepper as needed.
At this point you can gently mash a few more potatoes if you prefer a creamier texture or leave them whole if you enjoy little bites mixed in.
If the pasta looks too dry, add a splash of boiling or hot water and if it looks too runny, keep cooking until it thickens.
Switch off the stove and count to 10, then add the pecorino, provolone and a little extra rosemary.
Stir and toss until everything melts into the most delicious creamy sauce.