In a large container, dissolve salt and sugar in 2 quarts water to make the brine. Submerge chicken in brine and refrigerate at least 1 hour or up to overnight. Remove chicken from brine and thoroughly pat dry with paper towels.  

Position rack in lower-middle of the oven and preheat to 375˚F.  

Place chicken on a rack-lined rimmed baking sheet. Stuff shallots, garlic, and parsley in cavity of chicken. Thread a long wooden skewer through flaps of skin on either side of cavity. Rotate skewer and rethread back through skin flaps, repeating stitching as necessary to close the cavity. Brush breast-side of chicken with 1 tablespoon melted butter and season generously with pepper. Place chicken breast-side down on the rack, then brush back with remaining tablespoon melted butter and season generously with more pepper. Roast chicken for until golden brown and the thickest part of the thigh registers 165˚ F on an instant-read thermometer, 75 to 80 minutes. 

Remove roasting pan from oven and turn on the broiler. Using 2 large wads of paper towels, carefully rotate chicken to arrange it breast-side up in the rack. Return roasting pan to oven and broil until the breast-skin is crisp and browned, 3 to 5 minutes.  

Remove roasting pan from oven. Tip rack carefully to allow juices from chicken cavity to run into the pan. Transfer chicken to cutting board and let rest, uncovered. Remove rack from baking sheet, then carefully pour the juices into a serving bowl for an easy sauce. (Pro Tip: Stir some butter or chopped herbs into the pan juices.) 

Carve the chicken after resting for 10 to 15 minutes, then serve topped with the pan juices.

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