Preheat oven to 375°F. Scatter tortilla strips on a baking sheet and spray with cooking spray. Bake to deep golden then season with salt.
Heat a medium soup pot over medium-high heat with olive oil, 2 turns of the pan. Add onions, garlic, jalapeño, salt, pepper, cumin and coriander, and stir to tender, 5 minutes. Add tomatoes with green chilies, black beans, kale, stock and water, and bring to boil. Reduce heat and simmer a few minutes for soup to thicken a bit and flavors to combine.
To serve, pile some toasted tortilla pieces in a shallow bowl and top with radishes and avocado. Pour a few ladles of soup over and garnish with cheese, cilantro and scallions.