Deviled Eggs:
6 eggs (older eggs are better than farm fresh)
1 tablespoon butter, melted
1 tablespoon mayonnaise
1 tablespoon whole-grain mustard
1 teaspoon garlic confit oil or vegetable oil, plus more for drizzling
Salt and freshly ground black pepper
For the garlic confit: Cut the tops off of the tip of the garlic heads, leaving the root ends intact. Add to a small saucepan and cover with the vegetable oil. Cook gently over medium-low heat until the oil is infused and the garlic is soft to the touch, about 45 minutes (it should not come to a simmer). Remove the garlic heads from the oil and allow to cool prior to removing the softened cloves. Squeeze out the cloves from their skins and mash slightly; set aside. Reserve the oil.
For the deviled eggs: Lay the eggs flat in a saucepan and cover with water. Put the saucepan over medium-high heat and bring to a boil. Once at a boil, cover with a tight-fitting lid, turn the heat off and let the eggs sit for 12 minutes. Submerge or rinse in cold water until cooled.
Peel the eggs, cut lengthwise and separate the yolks. Mash the yolks in a bowl with the melted butter, mayonnaise and mustard until smooth. Stir in the oil and season with salt and pepper. Put the filling into a piping bag, no tip needed. Season the egg white halves with salt and pepper and drizzle with some of the garlic oil. Refill the egg whites with the filling.