Preheat oven to 425 degrees. Adjust oven rack to middle position. Using kitchen shears, cut along both sides of backbone to remove it. flatten breastbone and tuck wings behind back.
Using your fingers, gently loosen skin covering breast and thigh. combine lemon zest, sugar, and 1 teaspoon salt in small bowl. Rub 2 tablespoons zest mixture under skin of chicken. Season chicken with salt and pepper and transfer to roasting pan.
Season chicken can be refrigerated for 3 hours.Whisk broth, 1 cup water, lemon juice, and remaining zest mixture in 4 cups liquid measuring cup, then pour into roasting pan. ( Liquid should just reach skin of thighs.) roast until skin is golden brown and breast registers 160 degrees and thighs register 175 degrees. 45 minutes.
Transfer to carving board and let rest for 20 minutes. Carefully pour liquid from pan, along with any accumulated chicken juices, into saucepan, Skim fat, then cook over medium-high heat until reduced to 1 cup, about 5 minutes, Whisk cornstarch with 1 tablespoon water in small bowl until no lumps remain, then whisk into saucepan. simmer until sauce is slightly thickened, about 2 minutes. Off heat, whisk in butter and parsley and season with salt and pepper, carve chicken and serve,. Enjoy