Cook the bacon in the butter in a medium saucepan over low heat until it renders slightly, about 2 minutes. Add the onion, garlic and celery seed and cook until soft, about 4 minutes. Scatter the flour over the mixture and stir to coat. Gradually add the broth and the milk, whisking until smooth.

Add the potatoes and sliced broccoli stem; increase the heat to medium and simmer, covered, until slightly softened, about 5 minutes. Add the broccoli florets and season with 1/2 teaspoon salt. Continue cooking, uncovered, at a rapid simmer until the vegetables are tender, about 5 minutes; season with salt and pepper.

Meanwhile, position a rack in the upper part of the oven and preheat the broiler to high. Spread the mustard on each piece of baguette and top with a cheddar slice. Place on a baking sheet and broil until the cheese melts; serve with the soup.