Make cucumber water: Mix all the ingredients for the cucumber water. Refrigerate until you are ready to serve.

Preheat the oven to 400° F (205°C). Line a baking tray with parchment paper and set aside.

Make bechamel sauce: Melt butter in a medium saucepan over medium heat. Whisk in flour and cook, stirring constantly, for about 3 minutes. Gradually add milk, stirring well until the mixture is smooth. Cook, stirring, until the sauce is thickened.

Finish bechamel sauce: Season with a little bit of salt and pepper. Remove from heat and whisk in mustard and nutmeg. Set aside while you make the sandwiches.

Assemble sandwich: Spread each bread slice with a layer of béchamel, spreading it all the way to the edges. Top a slice of bread with a piece of ham, gruyere, and a sprinkle of parmesan cheese. Place another slice of bread on top, béchamel side up, then top with the remaining gruyere and parmesan cheese.

Repeat for remaining sandwiches.

Bake in the oven for about 5-6 minutes, until cheese is melted, and then turn the oven to broil and broil until the cheese on top is lightly golden, 2-4 minutes.

Prep carrot per instruction above.

Serve: Cut sandwich in half. Serve with carrots with hummus, and cucumber water.