Cut tortillas in half, then into thin strips. Heat oil in a medium saucepan over medium-high heat. Fry tortilla strips in batches until light brown and crispy. Remove and drain on paper towels.
In the same saucepan, cook chopped onion over medium-high heat for 2 minutes. Stir in garlic and poblano pepper, and cook until tender-crisp, about 2-3 minutes.
Add broth, diced tomatoes, and salt. Bring to a boil, then reduce heat and let simmer for 15 minutes.
Stir in shredded chicken and heat through.
Divide half of the tortilla strips among 4 serving bowls. Ladle in soup, then top with avocado slices.
Garnish with remaining tortilla strips, chopped cilantro, and a drizzle of spicy yogurt. Serve hot.
Notes
Store leftovers in an airtight container for up to 3 days. Keep tortilla strips separate to retain crunch.