In a large pot, bring the chicken stock and water to a bubble with the reserved corn cobs and let simmer for about 10 minutes.
Place the corn tortilla strips onto a baking sheet and spray them with some cooking spray. Transfer to the oven and bake until crispy, 10 minutes.
Preheat a skillet over medium-high heat with some EVOO about 2 turns around the pan. Add the chicken, browning on all sides, then place into the oven for about 7-8 minutes, until juices run clear and no pink remains in the center. Once the chicken is done cooking, remove from oven and let rest before cutting into strips. (I'd just cook the chicken in the same pot I'll cook the soup in- why mess up another pan?).
Preheat a heavy-bottomed pot with remaining 2 tablespoons of EVOO. Add the onion, garlic and cumin, and cook till soft, about 3-4 minutes. Add the corn kernels along with the jalapeño.
While the veggies are cooking, puree the tomatillos in a food processor until somewhat smooth. Add the purée, stock and chicken to the pot along with the veggies.
Simmer for 10-15 minutes. Remove the soup from the heat and add in the cilantro, lime zest and juice, and serve it up garnished with a big handful of jack cheese, tortilla and avocado.