One 3- to 4-pound chicken, rinsed and patted dry
3 tablespoons kosher salt
3¼ cups all-purpose flour, plus extra for rolling
1½ tablespoons sugar
1 pound unsalted butter, chilled and cut into 1-inch pieces
¾ cup cold water
1 tablespoon finely chopped fresh sage
1 tablespoon finely chopped fresh thyme
2 large eggs, beaten
1. Rub the chicken all over with 2 tablespoons of the kosher salt. Wrap with plastic wrap and refrigerate for 6 to 8 hours.
2. Make the dough: In a food processor, combine the flour, sugar and the remaining salt. Add the butter and pulse until the mixture looks like coarse meal with butter pieces no larger than a small pea. Transfer the flour mixture to a bowl, add the water and continue to mix until the dough comes together.
3. Turn the dough out onto a sheet of plastic wrap and pat into a 1-inch-thick circle. Enclose in plastic wrap and refrigerate for at least 1 hour (or up to 2 days; if chilling the dough for more than 30 minutes, let it sit out at room temperature for 10 minutes before rolling).
4. Meanwhile, set the chicken on a cutting board and, using kitchen twine, tie the bases of the drumsticks together, slightly crossing one drumstick over the other. Tuck the wings behind the back and set the chicken aside.
5. Roll out the dough to a diameter of 8 inches, sprinkle evenly with the sage and thyme and then fold into thirds (like a letter). Roll the dough into a 14-inch square about ¼-inch thick. Cut the corners out of the dough (roughly a 3-inch square out of each corner) so that it resembles a cross (reserve dough scraps for another use). Place the chicken, breast side down, in the center of the cross. One at a time, fold the dough flaps over the chicken, brushing the edges of the dough with the beaten egg to seal, to enclose the chicken in the dough. Transfer the chicken, breast side up, to a parchment paper-lined sheet tray. Using your hands, mold the dough to the form of the chicken. Brush the rest of the dough with the remaining beaten egg and refrigerate for 30 minutes.
6. Preheat the oven to 400°. Roast the chicken, rotating the pan occasionally, until the dough is golden brown and an instant-read thermometer inserted into the thigh joint (through the dough) registers 175°, about 1 hour and 45 minutes.
7. Remove the chicken from the oven and transfer to a cutting board. Let it rest for 10 minutes before carving.