Melt the shortening in a large saucepan over medium-high heat. Add the meat and brown well on all sides.
Add the onions and saute for 5 minutes, or until tender.
Add the canned tomatoes, jalapeno chile peppers, fresh tomatoes, cumin, garlic, and salt and pepper to taste.
Reduce heat to low, cover and simmer for 30 minutes to 1 hour, or until meat is tender. (If mixture is too thick, add water as needed. Or if mixture is too thin, combine some cornstarch and water and add to thicken.)