First of all, chop the onion and cut the carrots and tomatoes into small pieces.
Pour all the vegetables into a large pot that can subsequently contain the potatoes and pasta.
Add the oil and let it brown over medium heat, stirring occasionally for a few minutes.
In the meantime, peel the potatoes, wash them, and cut them into cubes about the same size as the vegetables and add them in the pot.
Brown them with the veggies for a couple of minutes, add some stock and cook for about 30 minutes at low heat. You want to make sure the stock covers the potatoes.
When potatoes are almost ready, add your optional parmigiano crust, a couple of glasses of water, and your pasta. Cook on medium heat allowing the pasta to fully cook and absorb all the starch in the potatoes while constantly mixing with a wooden spoon. Gradually add more water if your mixture is too dry.
Dice the provolone nice and finely and add it to the pasta once it’s ready.