Once the eggs are fully cooled, peel them and set aside. Make sure they are completely cool before going into the jar, as warm eggs will cloud the brine.
Place the peeled hard boiled eggs into a clean glass jar large enough to hold all of them.
Add the sliced garlic, jalapeño if using, and onion rings into the jar, tucking them in between and around the eggs so the aromatics are evenly distributed throughout.
In a medium saucepan, combine the white vinegar, water, sugar, salt, hot sauce, black peppercorns, red pepper flakes, mustard seeds if using, and celery seed if using.
Bring the mixture to a simmer over medium heat, stirring occasionally until the sugar and salt have fully dissolved, about 3 to 5 minutes.
Remove the saucepan from the heat and allow the brine to cool for 15 minutes. You want it warm but not at a rolling boil when it hits the eggs, as boiling hot liquid can toughen the whites.
Carefully pour the warm brine over the eggs in the jar, making sure all eggs are fully submerged. If any egg is peeking above the brine, press it down gently or place a small ramekin on top to keep everything under the liquid.
Seal the jar with a lid and transfer to the refrigerator. Allow the eggs to pickle for at least 24 hours before eating. For the best flavor, wait 2 to 3 days. The heat and tang deepen significantly with time.
Eggs will keep refrigerated in a sealed jar for up to 2 weeks.