Step 1: Hard-cook the eggs. Place in a large saucepan with cold water to cover by 3 inches. Bring to a boil over high heat, then reduce the heat to a simmer and cook the eggs for 11 minutes (a few minutes longer if you live at a high altitude). Fill the pan with cold water, then shell the eggs. (It’s easier to shell the eggs when still warm.) Return to the cold water to cool, then drain well and blot dry. The eggs can be boiled up to 48 hours ahead.
Step 2: Set up your smoker following the manufacturer’s directions. Add the wood as specified by the manufacturer.
Step 3: Smoke the eggs until bronzed with smoke, 20 to 30 minutes when hot smoking, 1 hour when cold smoking. Let cool to room temperature.
Step 4: Cut a thin slice off each end of each egg (this helps the halves stand upright). Cut the eggs in half widthwise through their equators. Pop out the yolks and place them in a food processor with the white scraps. (Alternatively, you can mash the yolk mixture with a fork.)
Step 5: Add the mayonnaise, mustard, Worcestershire sauce, and sriracha and puree to a thick paste. Spoon this mixture back into the egg white halves. Sprinkle the tops with chives and/or smoked paprika. Or top with salmon caviar or shredded brisket, bacon, or pork. Chill until serving.