Tomato-Cheddar Soup with Ham Toasties

In this riff on the classic combination of tomato soup and grilled cheese, the cheese is melted into the soup itself. The ham sandwiches, served on the side, are perfect for dunking.

• 3 oz. (6 Tbs.) unsalted butter, softened
• 1 small sweet onion, such as Vidalia, coarsely chopped (about 1-1/4 cups)
• 2 medium cloves garlic, coarsely chopped
• 1 large sprig fresh thyme
• 1/2 cup dry white wine (optional)
• 2 14-oz. cans diced fire-roasted tomatoes and their juice
• 2 cups lower-salt chicken broth
• Kosher salt and freshly ground black pepper
• 8 slices country white sandwich bread
• 8 slices deli ham, preferably Black Forest
• 2 Tbs. Dijon mustard
• 1/2 cup heavy cream
• 4 oz. sharp Cheddar, finely grated (2 cups using a rasp grater)

Position a rack in the center of the oven. Put a baking sheet on the rack and heat the oven to 400°F.

Melt 2 Tbs. of the butter in a 3-quart saucepan over medium-low heat. Add the onion, garlic, and thyme and cook, stirring occasionally, until the onion softens, about 5 minutes.

Turn the heat to medium high, add the wine, if using, and cook until reduced by half, about 3 minutes.

Add the tomatoes, chicken broth, 1 tsp. salt, and 1/2 tsp. pepper and bring to a boil. Lower the heat, cover, and simmer, stirring occasionally, for 10 minutes to meld the flavors.

Meanwhile, make 4 sandwiches with the bread, ham, and mustard. Butter the outsides of the sandwiches with the remaining 4 Tbs. butter and transfer to the hot baking sheet. Bake, flipping once, until golden-brown on both sides, 6 to 10 minutes.

Remove the thyme sprig from the soup and blend the soup with an immersion blender or in batches in a blender until smooth, about 2 minutes. Return the soup to the pot, stir in the cream, and bring just to a simmer over medium heat. Reduce the heat to low and stir in the cheese, a handful at a time, until melted. Season to taste with salt and pepper.

Serve the soup with the sandwiches.