Bring the vinegar, 3/4 cup water, 3 tablespoons salt, the coriander seeds, mustard seeds, sugar, onions and chiles to a boil in a medium saucepan over medium heat, stirring to dissolve the salt and sugar. Reduce the heat, cover and let the brine simmer for 5 minutes.
Meanwhile, pierce each egg all the way through about 6 times with a cake tester or toothpick. Put 2 eggs in each of 3 glass pint jars with lids, and tuck the celery and dill in around them. Ladle in enough brine to cover the eggs, add 2 more eggs to each jar and ladle in more brine to cover, leaving about 1/4 inch of space at the top. Close the jars, let cool to room temperature and refrigerate for at least 24 hours before serving.
To serve, halve or quarter the eggs, and spoon some pickling liquid and vegetables over the top. (The eggs will keep, covered by liquid and refrigerated, for up to 5 days.)
Copyright 2015 Television Food Network, G.P. All rights reserved.