Put a pot or a dutch oven over medium heat. Add the Extra-Virgin Olive Oil (3 tablespoon) and allow to get hot, then add the Carrot (1/2 cup), Yellow Onion (1), Celery (1/2 cup), Garlic (3 clove), and salt. Stir and cook until the vegetable softened a little, about 5 minutes.
Add Ground Beef (1 pound), breaking it up with a spoon, add Salt and Pepper (to taste). Cook until the meat has begun to brown, 5-7 minutes.
Add Tomato Paste (2 tablespoon) and stir until is mixed with the meat. Add Tomato (26 ounce) rinse the box with Water (1 cup) and add it in, add Dried Basil (1 1/2 teaspoon) and mix together. Bring the sauce to a boil, then reduce heat to low, cover and simmer for three to four hours.
Once the sauce has finished cooking, taste it, and adjust the seasoning to your liking. Then add half of the sauce to cooked Fettuccine (1 pound) and toss to coat.
To serve, place pasta in shallow bowls and spoon the rest of the sauce over the pasta and grate Parmigiano-Reggiano (to taste) on top.