Using a small food processor, mince the vegetables.
Heat the olive oil in a large saucepan over medium heat. Add the onion, carrot, and celery. Sauté gently, stirring often, until the vegetables are soft and fragrant—about 8-10 minutes.
Add the garlic and cook for another 1-2 minutes, avoiding browning to keep the sauce sweet.
Add in the wine and gently deglaze the pan allowing the wine to evaporate a bit.
Pour in the tomatoes and stir well. Season with salt and add basil leaves.
Bring the sauce to a gentle simmer, then reduce the heat to low. Cover and cook slowly for about 30 minutes, stirring occasionally.
Adjust seasoning with salt and pepper to taste.
Using a handheld blending stick, blend the sauce into a smooth texture. Alternatively you can pour the sauce into a blender and blend the sauce that way.
When serving, cook the pasta with the sauce until it is evenly coated. Sprinkle the pasta with pecorino cheese and pepper. Enjoy!