Meanwhile, heat a large skillet over medium heat. Melt the butter and add the breadcrumbs. Stir until breadcrumbs are golden brown and toasted, about 5 minutes. Let cool then fold in the chives. Set aside.
Remove the shell from each egg and slice in half lengthwise. Use a spoon to remove the yolks to the bowl of a blender.
Add the cream cheese into the blender and blend until smooth. Transfer to a piping bag.
Pipe the egg yolk mixture into hollows of the egg whites.
Sprinkle with everything bagel seasoning and bread crumbs. Serve immediately.