Begin by preheating the oven to 400 degrees and greasing a 9x13 casserole dish. To a sheet pan, add the baguette cubes and toast on the upper oven rack until lightly browned, 8-10 minutes. Add evenly to the bottom of the casserole dish. Sprinkle shaved ham evenly atop the toasted bread cubes and set aside.
Next prepare the GF Béchamel Sauce. To a medium saucepan over low heat, add the butter to melt. Whisk in the flour and cook on low for 1-2 minutes to form a roux. Slowly stir in the milk, whisking constantly, and allow mixture to reach a simmer. Stir in salt, pepper, nutmeg, dijon and thyme. When mixture is bubbling and thickening, continue to whisk and add in parmesan until very thick and mixture coats the back of a spoon. Set aside to cool while preparing the egg custard.
To a large bowl, crack in the eggs, cream, dijon, salt, pepper and nutmeg and whisk together until well combined. Stir in the shallots and chives.
To the casserole dish with the cubed baguette and ham, spoon atop 1/2 of the béchamel sauce uniformly. Next, pour the egg custard atop.
Finish with adding the rest of the béchamel sauce atop the egg mixture followed by the grated gruyere. Bake on the middle rack of the oven for 20-35 minutes, until just puffed in the center and golden.
Let cool 5-10 minutes before serving. Serve topped with more sliced chives and enjoy.