Season chicken strips with the cumin, coriander, and chili powder.
Heat 2 tablespoons oil in a 4-quart or larger soup pot over medium-high heat, add chicken, and cook until browned, about 5 minutes. Add onion, garlic, poblano, jalapeno, cilantro stems, and 1 1/2 teaspoons salt and cook, stirring as needed, 10 minutes, or until onions are soft and lightly caramelized. Add tomato paste and cook 1 minute longer. Add stock. Increase heat to high and bring to a boil; reduce heat to a simmer and cook for 20 to 40 minutes. Remove cilantro stems, stir in lime juice, and remove from the heat.
In a 12-inch or larger saute pan, heat 2 inches of vegetable oil to 370 degrees. Fry tortilla strips in batches, stirring frequently with a slotted spoon or strainer, until golden and crisp, 1 1/2 to 2 minutes. Remove from oil and set aside on paper towels to drain. Season tortilla strips lightly with salt.
Crumble a large handful of tortilla strips and gently stir into soup, to thicken. Ladle soup into bowls. Garnish with additional lime juice, cilantro leaves, avocado, grated cheese, and fried tortilla strips.