To roast the garlic, preheat the oven to 350 degrees F. Slice off the top portion of the garlic head to reveal the cloves. Lightly rub back and forth to remove the paper and peel any excess paper off. Pour a bit of the oil over each bulb. Wrap the bulbs tightly in foil and place in the oven. Roast for 45 to 60 minutes, until the cloves are caramel and golden in color. You can do this process ahead of time!
Once fairly cooled, squeeze the cloves out into a bowl and mash them with a fork, adding a pinch of salt.
To make the cheese straws, preheat the oven to 400 degrees F. Line a baking sheet with parchment paper.
Place 1/3 cup of cheese on the surface and place your sheet of pastry down. Cover it with 1/3 cup of cheese and roll it out with a rolling pin, pressing the cheese into the pastry and thinning it out. Rub half of the roasted garlic over top and then add another 1/3 cup of cheese. Fold the pastry in half and add another sprinkle of cheese on top, then roll it out again until it’s pretty thin. Slice the pastry into 1-inch strips and twist them, placing them on the baking sheet. Repeat with the other sheet of pastry.
Place the baking sheet with the twists into the freezer and chill for about an hour before baking.
Bake the straws for 15 to 20 minutes, until golden and puffed. Remove from the sheet and serve!