In a small saucepan, add vinegar, water, sugar, salt, mustard, mustard seeds, turmeric, peppercorns, celery seed, and garlic. Set over high heat and bring to a simmer. Simmer for 5 minutes, or until sugar and salt have fully dissolved.
Remove saucepan from heat and let cool to room temperature, speeding the process in the refrigerator or freezer if you prefer.
Layer hard-boiled eggs and onion slices in a large glass jar until full, then pour cooled brine into jar to cover. Be sure to get garlic and seasonings into jar with brine, then discard any excess brine.
Seal jar and store in refrigerator for one week, then enjoy.