Heat olive oil in large pot or cast iron skillet. Add onion and sauté until translucent. Add garlic and sauté slightly without browning.
Add chicken, tomatoes, stock, cumin and oregano. Bring to a boil and then reduced to simmer. Continue cooking until chicken is done.
While soup is cooking, cut tortillas into ½-inch strips. Heat ½ inch oil in a skillet until a test tortilla strip sizzles when dropped into oil. Fry tortilla strips one layer at a time. Watch carefully so not to burn. Remove with tongs and drain on paper towels. Repeat until all are fried.
To serve: place fried tortillas in bottom of serving bowls. Pour in soup and garnish with grated cheese and a few sprigs of cilantro.