Preheat the oven to 350°. Spread the walnuts in a pie plate and toast for 12 minutes, until golden. Let cool, then coarsely chop.
In a large skillet, melt the butter in the oil. Add the onion and cook over high heat, stirring, until softened, 4 minutes. Add the cabbage and vinegar, season with salt and pepper and cook, stirring occasionally, until the cabbage is barely wilted, 6 minutes. Add the thyme and the water, cover and cook over low heat, stirring occasionally, until the cabbage is tender and the water has evaporated, 20 minutes. Stir in the Thyme-Scented Pearled Barley, ricotta salata and toasted walnuts. Transfer to a bowl and serve.