Rinse, core, blanch, peel and dice the tomatoes.
In a large pot, preferably in a large cast-iron jambalaya pot, mix the tomatoes with the oil, salt, granulated garlic and onion, dried basil, and peppers. Taste and add sugar if the sauce tastes tart. Do not fill the pot more than 3/4 of the way. If your pot is too small, make your batches smaller.
If making meat tomato sauce, heat the 1/4 cup of oil and brown the ground beef. Then add the rest of the ingredients as described in the step above.
Bring to a boil, turn down the heat to medium-low and simmer, uncovered, frequently stirring, until the desired thickness is achieved. I usually stop when the sauce is about 3/4 of the original volume. This will take about 40 to 60 minutes.
Fill clean pint-size jars with the hot tomato sauce, leaving one-inch headspace. Wipe the rims and cover them with the lids. Tighten the bands finger-tight.
Process in a pressure canner for 60 minutes at 10 lb weighted gauge for 0 - 1000 ft elevations above sea level and 15 lb weighted gauge for elevations above 1000 ft. If using quart jars, the processing time should be increased to 70 minutes.
When the processing is done, turn off the heat and let the pressure canner depressurize on its own.
Remove the jars and let them fully cool down at room temperature. Check the jars to ensure that each is properly sealed. Store in a cool, dry, and dark place. Properly sealed and stored tomato sauce will keep its freshness for at least a year and up to 2-3 years before noticeable loss of taste qualities.
Refrigerate the tomato sauce once the jar is open.