Step 1

Pat the beef dry with a paper towel; sprinkle with the pepper. Heat 1 tablespoon of the oil in a large nonstick skillet over medium-high. Add the beef to the skillet; cook, stirring occasionally, until lightly browned on all sides, about 4 minutes. Transfer the beef to a 5- to 6-quart slow cooker. Add the carrots, onions, and remaining 1 tablespoon oil to the skillet; cook, stirring occasionally, until the vegetables are softened, 3 to 4 minutes. Transfer to the slow cooker.

Step 2

Add the wine to the skillet; cook over medium-high 1 minute, stirring and scraping to loosen the browned bits from the bottom of the skillet. Pour over the beef mixture in the slow cooker.

Step 3

Stir the stock, tomatoes, and pesto into the slow cooker. Cover; cook on HIGH 2 hours. Stir in the barley; cover and cook on HIGH until the beef and barley are tender, about 2 hours. Stir in the kale and salt. Ladle the soup into bowls, and serve hot.