Place the eggs in a single layer in a saucepan and cover with cool water by about 1 inch. Bring to a gentle boil over medium-high heat, then cover, turn off the heat, and let sit for 10–12 minutes to cook through without turning the yolks dry.

Transfer the eggs immediately to an ice bath and let sit for at least 10 minutes. Gently crack the shells all over and peel, running under water if needed. Pat dry.

Slice each egg in half lengthwise. Carefully pop the yolks into a medium bowl and arrange the egg white halves on a serving platter.

Use a fork to mash the yolks until very fine and crumbly, with no large lumps. The smoother they are now, the creamier the filling will be.

Add the mayonnaise, softened cream cheese, Dijon mustard, and lemon juice or vinegar to the mashed yolks. Mash and stir until completely smooth and thick. If the mixture seems too stiff, add 1/2–1 teaspoon water or a tiny splash of extra mayo and mix again.

Stir in the garlic powder, 1 tablespoon everything bagel seasoning, chives or green onions (if using), and a pinch of black pepper. Taste and add salt only if needed, plus more seasoning or lemon juice to taste. The filling should be slightly more seasoned than you think, since the egg whites will mellow the flavor.

Spoon or pipe the yolk mixture back into the egg white halves, dividing evenly. For a neater look, transfer the filling to a piping bag or zip-top bag with a corner snipped off and pipe swirls into each egg white.

Sprinkle the tops of the deviled eggs with extra everything bagel seasoning. Add a little chopped chive or a pinch of paprika or smoked paprika for color, if desired. Go light with the seasoning, as it is salty and crunchy.

Cover and refrigerate the deviled eggs for at least 30 minutes, or up to 24 hours, before serving. For the best texture and flavor, let them sit at room temperature for 10–15 minutes before serving.