Place eggs in a pot, cover with water and bring to full boil. Turn off heat, cover pot and let stand 10 minutes. Drain, crack eggs by shaking pot and run under cold water until cool enough to handle.
Peel eggs and halve lengthwise or trim tops and remove yolks to present eggs upright. You should have 12 upright eggs or 24 halved eggs.
To the hardboiled egg yolks, add grated onion, grating directly over bowl to catch the onion juice, garlic, relish, Worcestershire, mustard, hot sauce, salt, pepper, paprika, mayo – a few tablespoons to start, mash to very smooth, adding a bit more if too dry.
Cut a corner off a ziplock bag and fill with the deviled filling. Pipe into egg whites and garnish with a bulls-eye of thinly sliced red chili pepper.