1. Preheat oven to 400°. Brush 1 side of tortillas with 1 Tbsp. oil; cut tortillas in half. Stack tortilla halves, and cut crosswise into 1/4-inch-wide strips. Arrange strips in a single layer on a lightly greased baking sheet. Season with salt and pepper. Bake 15 minutes or until golden, stirring halfway through. Cool.
2. Meanwhile, heat a nonstick skillet over high heat 2 minutes. Add tomato halves, and cook, turning occasionally, 10 minutes or until charred on all sides. (Tomatoes may stick.) Transfer to a food processor.
3. Sauté onion in remaining 1 Tbsp. hot oil in skillet over medium heat 3 to 5 minutes or until tender. Add garlic; sauté 2 minutes or until fragrant. Transfer onion mixture to food processor with tomatoes; process until smooth.
4. Cook tomato mixture in a Dutch oven over medium-high heat, stirring occasionally, 5 minutes or until thickened. Stir in broth and tomato juice. Add bay leaf and next 3 ingredients; bring to a boil. Reduce heat to medium-low, and simmer, partially covered and stirring occasionally, 20 minutes.
5. Add chicken; simmer, stirring occasionally, 5 to 7 minutes or until chicken is done.
6. Discard bay leaf. Stir in green onions and next 2 ingredients. Season with salt and pepper. Divide queso fresco among 4 to 6 soup bowls; top with tortilla strips. Ladle soup into bowls. Top with avocado.