Make the filling
Halve the eggs and gently scoop the yolks into a medium bowl. Arrange the whites, cut side up, on a serving platter, and set aside. Add the mayo, shallots, fish sauce, vinegar, tom yum powder or paste, and a pinch of salt to the yolks in the bowl. Use a whisk, potato masher, or hand mixer to blend until smooth. Spoon the filling into a large Ziploc bag, force it into one corner, twist the top of the bag, then snip ¼ inch off the corner of the bag to create a makeshift pastry bag (of course, use a real one, with a ¼-inch fluted or plain tip, if you have one!).
Fill and garnish the eggs
Pipe a heaping scoop of the yolk mixture onto each egg white half, then top with a large piece of chicharron, and use a Microplane grater to finely zest lime straight onto the top of the eggs.