Grease a 9x13 baking dish. Layer the bottom halves of croissants in dish. Then layer the ham and Swiss cheese on top of the bread. Top the ham and Swiss with the top half of the croissants.
Whisk eggs, half and half, milk, 1 tablespoon spicy brown mustard, and salt together. Poke a few holes in the tops of the croissants with a fork, and then pour the egg mixture over croissants, making sure croissants are submerged.
Cover with foil and chill over night.
Remove the croissants from refrigerator 30 minutes prior to baking. Preheat oven to 350 F. Bake, covered with the foil, for 30 minutes. Uncover, and continue baking for an additional 25 to 30 minutes.
In a saucepan, mix butter, brown sugar, Worcestershire sauce, 2 tablespoons spicy brown mustard, and poppy seeds. Bring to a boil for 2 minutes. Pour over baked croissants.