Preheat oven to 400 degrees. Cut ¼ inch from the top of the garlic bulb, exposing the top of the cloves. Place garlic on a sheet of aluminum foil. Drizzle olive oil on top. Wrap the foil tightly around the garlic bulb. Place on a baking sheet and bake the garlic for 45-50 minutes until the gloves are tender and start to brown. Remove from the oven and cool completely.
Eggs
Add the eggs to a medium saucepan. Add enough cold water to just cover the eggs and cover with a lid. Bring the pot of water to a boil over high heat. Then, turn off the heat and let the eggs sit in the hot water. Leave the eggs in the hot water for about 10-15 minutes. Remove the eggs from the pot, add to a bowl of cold water, and cool completely. The eggs can be refrigerated overnight if desired.
Assembly
Peel the shells off each egg and rinse under cold water to ensure all of the shells are off. Slice each egg in half horizontally. With a spoon, remove all the the yolk halves and place into a food processor, or into a mixing bowl if making the filling by hand. Squeeze the whole garlic bulb so that the roasted cloves come out into the food processor. Add the mayonnaise, mustard, relish, truffle oil or paste and 1/2 tsp fresh dill. Cover and blend until the mixture is smooth. If mixing by hand, add all of the ingredients to the bowl and mash and mix with a fork until blended.Add mixture to a piping bag with a star tip and fill each egg white half with the mixture. Garnish with additional dill and with fresh oregano. Serve.