How to Make It
Heat oven to 400° F. Heat 1 tablespoon of the butter in a large pot over medium-high heat. Add the leeks, thyme, and ½ teaspoon each salt and pepper. Cook, stirring often, until very tender, 10 to 12 minutes. Add the broccoli, broth, and 2 cups water and bring to a boil. Reduce heat and simmer until the broccoli is crisp-tender, 6 to 8 minutes. Working in batches, transfer the mixture to a blender and puree until smooth.
Meanwhile, spread the remaining tablespoon of butter on the baguette. Top with the turkey and Cheddar, dividing evenly. Place on a baking sheet and bake until the Cheddar is melted, 4 to 6 minutes.
Serve the soup sprinkled with thyme leaves, with the turkey-and-cheese toasts on the side.