Add oil to a very large saucepan. Heat until shimmering over medium heat.
Add onion. Sauté in hot oil until transparent.
Add tomatoes. Cook, stirring until tomatoes are softened.
Remove from heat and allow to cool to warm.
Add tomatoes and onions to a blender or food processor. Purée until smooth. Return mixture to pan.
Add all other ingredients, except tortilla strips, salt and pepper, cheese and fried tortilla strips.
Simmer, stirring occasionally, for about 30 minutes.
Add tortilla strips and heat, stirring occasionally, for about ten more minutes.
Taste. Add salt and pepper, to taste, if needed.
Serve with cheese and fried tortilla chips, to top (See Note 2 Above).