Barley Gratin with Roasted Cherry Tomatoes

Name: Barley Gratin with Roasted Cherry Tomatoes
Ingredients: 5 tablespoons unsalted butter, plus more for greasing; 1 quart low-sodium chicken stock or broth; 2 cups pearled barley; Kosher salt; Pepper; 2 medium onions, finely chopped; 8 ounces cremini mushrooms, finely chopped; 1 teaspoon chopped thyme leaves; 1/2 teaspoon caraway seeds; 2 tablespoons all-purpose flour; 2/3 cup whole milk; 4 ounces Gruyère cheese, shredded (1 cup); 2 cups cherry tomatoes, halved; 4 ounces Saltine crackers, crushed (1 sleeve or 2 cups crushed); 1/4 cup freshly grated Parmigiano-Reggiano cheese