Preheat the broiler. If using fresh jalapeños, cut them in half and remove the seeds, then place cut side down on a baking sheet. Broil them for 1-2 minutes, until the skins blacken and bubble. Remove from the broiler. When cool enough to handle, peel off and discard the outer skin, then dice the peppers. Set aside.
Turn the oven to 400˚F (200˚C).
In a medium bowl, mix the cream cheese and sour cream. Add the cheddar cheese, ¾ of the Parmesan, and the diced jalapeños. Mix well.
In a separate medium bowl, mix the bread crumbs, melted butter, the remaining Parmesan cheese, and the parsley.
Spoon the jalapeño mixture into an 8x8-inch (20x20-cm) baking dish or a medium cast iron pan, spreading evenly. Sprinkle the bread crumb topping evenly on top.
Bake for 20 minutes, or until hot and the bread crumbs are golden brown. Serve with bread or crackers.