Heat the olive oil in a large Dutch oven over medium-high heat. Add the corn tortilla squares and fry, stirring occasionally, until they turn golden yellow and crisp, about 3 to 4 minutes.
Add the white onion, jalapeno pepper, and garlic to the pot. Cook, stirring frequently, for 1 to 2 minutes until the onion turns translucent and the garlic is fragrant.
Add half of the white corn kernels along with all remaining ingredients (tomatoes, tomato paste, cumin, kosher salt, ground white pepper, chili powder, water, and chicken stock). Reserve the remaining corn kernels for later. Stir to combine.
Bring the soup to a low, even boil over medium-high heat. Boil for 5 minutes, then remove the pot from the heat.
Use an immersion blender to process the soup in the pot to the consistency of a coarse puree (some texture is fine and desirable). Alternatively, transfer the soup in batches to a countertop blender. Use caution with hot liquid: fill the blender no more than halfway, hold the lid down firmly, and let steam escape slightly before blending.
Return the pot to medium heat and stir in the reserved white corn kernels. Bring the soup back to a boil, stirring constantly to prevent scorching on the bottom of the pot.
Ladle into bowls and serve immediately, garnished with blue corn tortilla chips, shredded cheddar cheese, and chopped cilantro.