This one's simple, simple, simple.
Start with your favorite recipe for deviled eggs: here's the first one that comes up in a quick Google.
Preheat the oven to 300F. Take a whole bulb of garlic and slice off the tip. Drizzle on a few drops of extra-virgin olive oil, wrap it in tinfoil cut side up, and roast it in the oven for an hour. Once it has completely cooled, squeeze it in your hand. The garlic will squirt out like toothpaste. Mix that into your deviled egg recipe. Voilà.