Begin by dicing the onion, carrot, and celery and set aside. Peel and chop one pound of potatoes into roughly one-to-two-inch cubes and set aside. Slice 3 ½ ounces of guanciale, if using, into small lardons or cubes and set aside. In a large pot, add 3 tablespoons of olive oil and heat to medium high.

Once heated, add the guanciale and onion and sauté until they turn translucent, about 5-7 minutes. In the meantime, in a small sauce pan or pot bring 4-6 cups of vegetable broth and/or water to a light simmer and keep to the side. Once the onion and guanciale have started turning translucent, add the carrot and celery and some salt and pepper and continue to sauté for about 5 more minutes.

Add 4 tablespoons of tomato paste and stir to combine with all the vegetables and let it roast for a minute or two before adding the potatoes. Add the potatoes and stir to coat in the oil and other vegetables, add some more salt and pepper, and let them cook for about 2 minutes. Now add enough broth to cover the potatoes, cover the pot, turn the heat to a simmer and allow to cook for about 20 minutes, until the potatoes are almost fork tender. Stir occasionally so that nothing sticks to the bottom and add more broth or water if needed.

When the potatoes are almost fork tender, add the pasta and enough broth or water to cover. Season with some more salt and stir everything. Turn the heat up to a strong simmer and cook, uncovered, until the pasta is al dente. Add more broth or water as needed to keep the pasta cooking and adjust for your desired consistency. Stir occasionally to keep things from sticking to the bottom.

Once cooked and your level of soupiness is achieved, remove it from the heat, and allow it to cool slightly. Serve in a bowl and garnish with grated pecorino Romano if desired.