For soffritto, blend carrots, celery, yellow onion, and 50 milliliters of olive oil in a food processor until well blended and smooth. Add 2 tbsp olive oil to a sauce pot on medium low heat. Add soffritto to sauce pot and cover bottom of the pan; cover pan with lid and simmer for 15 minutes. Remove cover and heat for another 5 minutes until soffritto is a light golden brown. Add tomatoes, salt, pepper, and mix well. Replace lid and simmer for 1 hour. Break up basil by hand. Remove lid, add basil and pecorino, stir well. Allow to simmer for another 45-60 minutes without lid so sauce thickens.