Preheat the oven to 375°F.

Using a sharp chef's knife, slice approximately ¼ of the top off each garlic bulb to expose the raw cloves inside. Discard the tops.

Place each garlic bulb cut-side up onto its own individual square of aluminum foil.

Drizzle the exposed cloves heavily with the olive oil, ensuring it seeps down into the bulbs. Season the exposed cloves evenly with the ground oregano, kosher salt, and coarse black pepper.

Loosely fold the aluminum foil up and around each bulb to create a pouch, leaving a small vent hole at the absolute top for steam to escape.

Place the foil pouches directly onto the middle oven rack or on a baking sheet. Roast until the garlic cloves are deeply golden, incredibly soft, and naturally pushing out of their papery skins, about 35 to 40 minutes.

Remove from the oven and allow the bulbs to cool to room temperature so they can be handled safely.

Place the softened unsalted butter into a small ceramic mixing bowl.

Squeeze the base of the cooled, roasted garlic bulbs to force the soft, caramelized cloves directly into the bowl with the butter. Discard the empty, papery skins.

Using a sturdy silver fork, aggressively mash the roasted garlic and softened butter together until they form a unified, highly textured compound paste.

Scoop the mashed garlic butter out of the bowl and place it into the center of a large sheet of heavy-duty plastic wrap.

Fold the plastic wrap over the butter and roll it tightly into a uniform, compact cylinder (log). Twist the ends of the plastic wrap tightly to seal the shape.

Place the wrapped butter cylinder into the refrigerator for at least 30 minutes to firm up and structurally reset.

To serve, use a sharp knife to slice the chilled cylinder into thick rounds (medallions) and place them immediately over screaming-hot grilled meats, fish, or roasted vegetables to melt.