Heat 1 tablespoon oil in 12-inch nonstick skillet over medium-high heat until shimmering. Add tomatoes, onion, half of jalapeños, garlic, tomato paste, 2 teaspoons chipotle, and 1/2 teaspoon salt and cook, stirring often, until onion is softened, 8 to 10 minutes. Transfer to slow cooker and wipe skillet clean with paper towels.
Tear 4 tortillas into 1/2-inch pieces. Add broth and tortilla pieces to slow cooker. Season chicken with salt and pepper and nestle into slow cooker. Cover and cook until chicken is tender, 4 to 6 hours on low.
Meanwhile, halve remaining 6 tortillas, then cut halves crosswise into 1/2-inch-wide strips. Heat remaining 1 cup oil in now-empty skillet over medium-high heat until shimmering. Add tortilla strips and cook, stirring occasionally, until golden brown, 4 to 6 minutes. Using slotted spoon, transfer strips to paper towel–lined plate. Season with salt to taste and let cool completely.
Transfer chicken to cutting board and shred into bite-size pieces with 2 forks. Whisk soup vigorously until tortillas are broken down, about 30 seconds. Stir in chicken, remaining jalapeños, and remaining 1 teaspoon chipotle. Season with salt and pepper to taste. Serve, passing tortilla strips, Cotija, cilantro, avocado, sour cream, and lime wedges separately.