Place tomatoes, onion, peppers, and garlic in a large food processor and process until chopped. Set aside.
Combine remaining ingredients in a large pot. Cook just below medium heat for 30-60 minutes, until the sauce is thick and dark. (If sauce is not thickening up at this point, add more cornstarch or arrowroot powder, stir and cook some more until thickened.) Remove from heat. Add chopped vegetables to sauce and stir until combined.
Ladle salsa into hot sterilized pint jars, leaving 1/2-inch headspace at the top. Seal with sterilized lids and process jars in boiling water bath for 35 minutes. (NOTE: If this is your first time canning, it would be worthwhile to either check out Canning 101 on the Ball website or one of the Ball canning books.)