This dish is a great way to use less-than-perfect summer tomatoes. A Parmesan cheese rind makes the chunky sauce extra savory and delicious.
Combine tomatoes, garlic, onion, tomato paste, Parmesan rind, and basil stems in a 5- to 6-quart slow cooker.
Sprinkle chicken thighs evenly with pepper and 1 teaspoon of the salt. Heat oil in a large skillet over medium-high. Add chicken to skillet, and cook until golden brown, about 2 minutes per side. Transfer to slow cooker, and nestle into tomato mixture. Cover and cook on LOW until tomatoes have broken down and chicken is very tender and done, 2 to 3 hours.
Transfer chicken to a cutting board to cool slightly. Remove and discard basil stems and Parmesan rind from slow cooker. Stir in remaining 1 teaspoon salt. Process mixture using an immersion blender until mostly smooth, about 30 seconds. Shred chicken into 1-inch pieces, and stir into slow cooker.
Toss pasta with tomato-chicken mixture, and divide evenly among 6 bowls. Top with basil leaves and grated Parmesan.