Place the peeled, chopped, and drained tomatoes and Kosher salt in a very large stockpot. Bring to a simmer, stirring frequently.
Use an immersion blender to coarsely blend the tomatoes until they reach your preferred chunky consistency.
While the tomatoes are simmering, combine the vinegar, lime juice, onions, jalapeños, garlic, and cilantro in a blender or food processor. Pulse until finely chopped but not completely pureed. Work in two or three batches if necessary. Add a small amount of the simmering tomatoes if additional liquid is needed for blending.
Add the blended onion mixture to the stockpot. Stir in the cumin, black pepper, tomato sauce, and tomato paste.
Simmer the salsa for 30 minutes to 1 hour, stirring frequently so the tomatoes and tomato paste do not scorch.
Ladle the hot salsa into hot canning jars, leaving the headspace specified by the validated process. Remove air bubbles, adjust the headspace, wipe the rims clean, and apply new lids and rings until fingertip tight.
Process the jars in a boiling-water canner for 40 minutes at elevations of 1,000 feet or less. Adjust the processing time for elevation. Begin timing only when the water reaches a full rolling boil.
When processing is complete, turn off the heat, remove the canner lid, and let the jars rest in the water for 5 minutes. Remove the jars without tilting and let them cool undisturbed for 12 to 24 hours.
Check the seals, remove the rings, wash and label the jars, and store properly processed jars in a cool, dry, dark place.