Heat butter in a heavy 8-inch skillet over medium heat. Add the onions and cook, stirring frequently, until they begin to soften, about 5 minutes. Cover and reduce the heat to medium-low.

Continue to cook, stirring occasionally, until the onions are soft and golden brown, 20 minutes longer. Adjust the heat so the onions brown but do not burn. Add balsamic vinegar, plus salt and pepper to taste, and cook for an additional minute. Remove from heat and set aside.

Put vegetable shortening and garlic cloves into a stockpot and cook over medium heat for 5 minutes. Then add remaining ingredients, including the onions, and simmer for 45 minutes. Allow mixture to cool.

Transfer cooled mixture to a blender and thoroughly puree. Return mixture to sauce pan and simmer for another five minutes.

This recipe yields about 8 cups.