Heat the oven to 400°F. Cut the top from the garlic head to expose the cloves, drizzle with olive oil, wrap in foil and roast for 35 to 45 minutes until very soft.
Cool garlic for 5 minutes, squeeze the softened cloves from their skins and mash them smooth. Mix with softened butter.
Spread half the garlic butter thinly over the inner faces of the bread. Divide provolone and Asiago between 2 slices and close with the other slices.
Spread remaining garlic butter thinly over the outside faces. Cook in a large skillet over medium-low heat for 4 to 5 minutes per side until golden and the cheese is fully melted, lowering the heat if the garlic butter darkens too quickly.
Rest for 1 minute, cut in half and serve.