Heat oil in a soup pot over medium heat. Brown sausage coins for 5 to 6 minutes, turning once, and transfer to a plate.
Cook onion and carrot in the pot for 6 minutes, then garlic for 30 seconds. Add barley, broth, thyme and pepper and bring to a simmer.
Cover partly and simmer gently for 30 to 40 minutes until barley is nearly tender, stirring occasionally along the bottom.
Return sausage and add kale. Simmer for 8 to 10 minutes until kale and barley are tender and sausage is heated through to 165°F.
Stir in cream and warm gently for 2 minutes without boiling hard. Divide among 6 bowls and serve promptly while the broth is still loose.