How to Make It
Heat 2 tablespoons oil in a large Dutch oven over high. Sprinkle chicken with pepper and 1 teaspoon salt, and cook until browned, 2 to 3 minutes per side. Remove chicken; let rest 5 minutes. Cut chicken into cubes, and set aside.
Reduce heat to medium-high. Add onion and celery, and cook, stirring occasionally, until tender, 3 to 4 minutes. Add garlic and basil, and cook, stirring often, 2 minutes. Add wine and tomato paste; bring to a boil, and reduce until liquid has almost evaporated, 3 to 4 minutes. Stir in stock. Add tomatoes, using your hands to crush tomatoes over pot as you add them. Bring to a boil. Add chicken, kale, tortellini, remaining 1/4 cup oil, and remaining 1 1/2 teaspoons salt. Simmer until tortellini are al dente, about 5 minutes.
Ladle soup into bowls. Top with Parmesan and additional basil.