Let the sliced Brie sit at room temperature while preparing the rest of the ingredients.
Prepare the ingredients as listed above.
In a small bowl, combine the butter, chives, parsley, Dijon mustard, and grated garlic. Mix well and season with salt and pepper to taste.
In another bowl, toss the arugula with lemon juice. Season with salt and pepper.
Slice the sub rolls or baguette pieces in half. Spread the herbed butter generously on the inside of each roll.
Layer the ham and Brie inside the bread. Season lightly with salt and pepper. Top with a handful of arugula, then cover with the other half of the roll.
In a pitcher, mix the lemon juice, water, and sugar until fully dissolved. Serve over ice if desired.
Serve the jambon beurre with potato chips, pickle spears, and a glass of fresh lemonade.