Preheat the oven to 375°F / 190°C.
Lightly coat a 9 x 13-inch casserole dish with butter.
Unroll the crescent roll dough.
Separate the dough along the perforated lines to form individual triangles.
Spread a small dollop of softened cream cheese onto each crescent roll triangle.
Roll each crescent roll triangle from the wide end toward the narrow end.
Arrange the filled crescent rolls evenly in the prepared casserole dish.
Place the rolls in 2 columns of 8 rolls each, if possible.
In a large mixing bowl, beat the eggs and whole milk until fully combined.
Add the shredded cheese, cubed ham, finely chopped jalapeño, freeze-dried parsley, ground pepper, and sea salt.
Stir until all ingredients are evenly distributed. The mixture will be chunky.
Pour the egg mixture carefully and evenly over the crescent rolls.
Use a fork or clean hands to gently distribute the ham, cheese, jalapeño, and egg mixture throughout the casserole dish.
Ensure the mixture reaches the edges of the dish and is evenly spread around the crescent rolls.
It is acceptable if some crescent roll tops remain slightly exposed above the egg mixture.
Place the casserole dish on the middle rack of the preheated oven.
Bake for 30 to 40 minutes, or until the casserole is puffed, golden brown, and fully cooked through.
If the top browns too quickly, loosely cover the dish with foil during the remaining baking time.
Remove the casserole from the oven.
Allow the casserole to rest for 5 to 10 minutes before slicing.
Slice into 16 portions.
Serve warm.