In a food processor or blender, purée tomatoes in their juices. In large (4-quart or larger) saucepan, heat 2 tablespoons oil over medium heat. Add chicken and cook 3 minutes on each side. Transfer chicken to a plate. Add and heat remaining 1 tablespoon oil. Add onion and cook, stirring frequently, until golden. Add garlic, chili powder and cumin. Cook, stirring frequently, for 1 minute. Add chicken stock, puréed tomatoes, tomato paste, chilies and jalapeños. Return chicken to saucepan, bring to boil. Reduce heat, cover and simmer 20 to 30 minutes. Transfer chicken to cutting board, cut into bite-sized pieces and return to saucepan. Continue simmering, uncovered, until ready to serve. In a large skillet, heat 1/2 inch of vegetable oil over medium-high heat. Add tortilla strips in batches and cook, stirring frequently, until crisp, 1 to 2 minutes. Transfer tortilla strips to paper towel to drain. Skim the surface of the soup and season with salt and pepper to taste. Divide tortillas among 4 soup bowls and ladle soup over tortillas. Sprinkle with chopped cilantro and Parmesan cheese.