Place a heavy bottom pot over medium high heat. Add 2 tablespoons of butter and olive oil. Once the butter is melted add the onion, garlic and thyme. Cook for about 5 minutes, stirring occasionally until the onion is soft and translucent.
Stir in the squash. Cook, stirring occasionally for about 6-8 minutes. Stir in the barley.
Add the white wine and stir. Cook until most of the wine has evaporated.
Add 2 cups of warm chicken stock (enough to cover the barley by about 1 cm) and bring to a simmer. Cover and cook for 10 minutes, stirring occasionally.
Add another 1 cup of warm stock to the barley, bring back to a simmer. Cover and cook for another 10 minutes, stirring occasionally.
Remove the lid and add another 1 cup of warm stock. Bring to a simmer, and cook uncovered this time for 5 minutes, stirring occasionally.
Stir in the frozen kale. Cook until it is thawed. Test the barley for doneness. The barley should be tender.
Stir in the parmesan cheese and remaining 1 tablespoon of butter until both are melted. Taste and season with salt and pepper. Serve immediately.