Preheat the broiler to low. Let the sliced Brie sit out at room temperature while you prepare everything.
Make the soup: Heat the butter in a pot over medium heat. Sauté the onions and garlic until the onions start to soften. Stir in the flour and cook for 1-2 minutes.
Stir in the broth, broccoli, and scallions. Season with salt and pepper. Cover with a lid and bring to a simmer for about 20 minutes, stirring occasionally. While the soup is cooking, make the sandwich.
In a small bowl, combine softened butter, minced chives, minced parsley, Dijon mustard, grated garlic, salt, and black pepper. Mix well to combine. Adjust seasoning to taste.
In another bowl, toss arugula with lemon juice. Season with salt and black pepper.
Spread the prepared butter mixture generously inside the bottom half of each baguette.
Layer the sliced ham and Brie cheese pieces over the buttered baguette.
Season the filling with a pinch of salt and black pepper.
Top with a handful of arugula.
Cover with the remaining half of the baguette.
Repeat the process for the remaining sandwiches.
Cut the sandwiches in half diagonally.
Mix the sparkling water and lemon slices together. Serve over ice if desired
Finish the soup: Stir the cream and cheese into the soup until it melts completely. Taste and adjust the seasoning with salt if needed.
Portion the soup and serve with ½ jambon beurre, chips and lemon sparkling water.