Hard-boil the dozen eggs using your preferred method; the most basic is to cover with cold water; bring to a boil; remove from the heat; let stand, covered, for 8 to 10 minutes.
Drain and cool the eggs in an ice bath and peel.
Slice the eggs in half lengthwise; use a small spoon to pop out the yolks and place in a bowl.
Cut the cream cheese into rough pieces and add to the yolks.
Use a hand beater or stick blender to blend, starting on low speed and then on high speed, until fluffy and whipped.
Beat in the salt and pepper; taste to adjust seasonings, if desired.
Use a spoon or a piping bag to fill the egg whites with the yolk mixture; it will be stiff; if necessary, microwave in very short bursts of 2 to 3 seconds to soften even more.
Sprinkle the tops of the filled eggs generously with the everything bagel seasoning.