Over medium-high heat, fry tortilla squares in olive oil until they begin to crisp and turn a golden yellow. Add garlic, onion and jalapeno; cook 1 to 2 minutes, until onion becomes translucent.
Add half the corn along with all other ingredients (except garnishes), reserving other half of corn to be added at the end. Bring the soup to a low, even boil. Boil for 5 minutes. Remove soup from heat.
Use a hand-held propeller blade processor to process in batches to the consistency of a course puree. You can also process in batches in a blender. Return the soup to the burner and add the reserved corn. Bring the soup to a boil once again being extremely careful to avoid scorching or burning the soup. Serve, garnished with blue corn tortilla chips, cilantro and sharp cheddar cheese.