Saute the onion, carrot, and garlic:  Get out a large pot and add the 5 tablespoons of olive oil to it.  Then place this pot on your stove, over a medium high heat. Once the pot has heated up for a minute toss in the onion, and carrot, sauteing them for about 3 minutes, or until the onion begins to become translucent.  Finally add in the minced garlic, and saute everything for another minute.

Add the tomatoes:  Toss in the cans of tomatoes along with the oregano, the black pepper, and a half cup of water.  Stir everything together and let it come to a boil. Once the sauce has come to a boil, lower the heat to medium low, and allow everything to simmer for 30 minutes to an hour.

Mash or blend the sauce: Now depending on how chunky or smooth you prefer your sauce you can approach this next step in two ways.  If you prefer a more rustic and chunky sauce then you can use a potato masher to mash the tomatoes until they are in small pieces.  However, if you prefer a cleaner, and smoother sauce then you can blend it. Either way is great it all just depends on your preference.

Store the sauce:  Get out 2 quart sized jars, and make sure that they are clean and sanitized.  Then take about 5 to 7 basil leaves and rip them up into smaller shreds, and then distribute them amongst the two empty jars.  Next pour the hot sauce over the basil in the jars (the residual heat of the sauce should cause the oils of the basil to distribute its flavor).  Finally close the jars, and store them in your refrigerator.