Step 1

Lightly butter an 8-inch square glass or ceramic baking dish. In a medium saucepan, combine the stock with the barley and 1 tablespoon of butter. Season with salt and pepper and bring to a boil. Cover and cook over low heat until the barley is tender, about 15 minutes. Do not drain.

Step 2

Meanwhile, in a large skillet, melt 2 tablespoons of the butter over moderate heat. Add the onions, mushrooms, thyme and caraway. Season with salt and pepper and cook, stirring occasionally, until caramelized, about 15 minutes. Transfer to a large bowl and wipe the skillet clean.

Step 3

Preheat the oven to 375°. In the same large skillet, melt the remaining 2 tablespoons of butter over moderate heat. Stir in the flour and cook, whisking constantly, until a paste forms, about 1 minute. Gradually whisk in the milk until smooth and thickened, about 4 minutes. Add the Gruyère cheese and cook, stirring, until smooth, about 2 minutes. Stir in the barley along with the reserved cooking stock, the onions and mushrooms. Season with salt and pepper.

Step 4

Scrape the barley mixture into the prepared pan and top with the tomatoes, crackers and Parmigiano-Reggiano cheese. Bake for 20 minutes, until golden and bubbling around the edges. Serve warm.