Heat butter and olive oil in heavy saucepan until butter melts. Add onion and cook until translucent. Add tomatoes and continue to cook until soft. Add jalapeno and mixed vegetable juice. Bring to boil and add stock and hot water. Bring to simmer.
Add cumin, paprika, chili powder, white pepper and garlic, and cook, stirring occasionally. Add tomato paste and 1/4 cup cilantro and cook, stirring occasionally. Mix cornstarch with 1 tablespoon water, then stir into tomato mixture and simmer until liquid is shiny, about 10 minutes.
Meanwhile, cut tortillas into 1 1/2-inch strips or cubes and deep-fry in hot oil. Remove and drain.
To serve, distribute 1/2 cup avocado, 1 cup chicken breast, 1/8 cup chopped cilantro and half tortilla strips among 6 bowls. Pour hot soup over garnish and top with remaining avocado, chicken breast, chopped cilantro and tortilla strips. Pass grated cheese on the side.