For brining the turkey
1 cup kosher salt
1 cup sugar
2 boneless turkey breasts, 3 to 4 ½ pounds each
For the glaze
8 heads garlic, lightly smashed but intact
4 teaspoons extra virgin olive oil
½ cups honey
1 tablespoon kosher salt
1 tablespoon freshly ground black pepper
1 tablespoon thyme leaves
To brine the turkey: In a medium saucepan, bring 1 quart water to a boil with the salt and sugar. Pour into a large pot, and add 3 quarts cold water.
Once the brine is cool, submerge the turkey breasts and refrigerate overnight, or up to 24 hours.
To make the glaze: Heat oven to 375° F. Toss the garlic heads with the olive oil in a small casserole dish, cover and roast until the garlic is soft, about 1 hour and 10 minutes.
Leave covered until cool enough to handle, then squeeze the garlic cloves from their skins into a food processor and purée.
Add the honey, salt, and pepper and blend once more. Cover until ready to use.
To cook the turkey: Heat oven to 250° F. Remove the breasts from the brine, pat dry, and wrap each one four times in plastic wrap and once in aluminum foil.
Insert an oven-safe thermometer into the center of one breast and place both on a wire rack in a roasting pan. Add water to reach to just below the rack.
Cook until the internal temperature reaches 135° F, 2 to 3 hours. Near the end of cooking time, fill a large bowl halfway with ice water.
Remove the turkey from oven and raise temperature to 425° F. Without removing thermometer or wrapping, submerge the turkey in the ice bath for 5 minutes.
Remove foil, plastic wrap, and turkey skin. Pat dry and brush glaze liberally on all sides of the breasts.
Roast until glaze is golden, 15 to 20 minutes. Sprinkle with fresh thyme and serve thinly sliced, hot or cold.