Tear the croissants into medium pieces and spread them evenly in a greased 9x13-inch baking dish.
Sprinkle the diced ham evenly over the croissant pieces.
Add 1 ½ cups of the shredded cheese, distributing it evenly over the ham and croissants.
In a large bowl, whisk together the eggs, half-and-half, Dijon mustard, garlic powder, onion powder, salt, and pepper until well combined.
Pour the egg mixture evenly over the croissant, ham, and cheese layers. Gently press down the croissant pieces to ensure they are soaked in the egg mixture.
Sprinkle the remaining ½ cup of shredded cheese on top.
Mix the melted butter with the everything bagel seasoning. Evenly sprinkle this mixture over the top of the strata.
Cover the dish with plastic wrap and refrigerate the strata for at least 4 hours or overnight. This step is crucial for allowing the croissants to absorb the egg mixture.
Preheat the oven to 350°F (175°C).
Remove the strata from the fridge, uncover, and let it sit at room temperature for about 15 minutes before baking.
Bake uncovered for 45-55 minutes, or until the top is golden and puffed, and the center is set (a knife inserted in the center should come out clean).
Let the strata rest for 10-15 minutes before serving. Garnish with fresh herbs, if desired.