Adjust oven rack to middle position and heat oven to 400 degrees. Stir 2½ teaspoons salt and pepper together in small bowl. Place chicken breast side up on cutting board. Using kitchen shears, thoroughly trim excess fat and skin from cavity. Lift 1 drumstick and use paring knife to cut ½-inch slit in skin where drumstick and thigh meet. Turn chicken on side so breast faces edge of counter. Cut ½-inch slit in skin where top of thigh meets breast. Repeat both cuts on opposite side of chicken. Tuck wingtips behind back. Sprinkle about one-third of salt mixture into cavity. Brush top and sides of chicken with melted butter. Sprinkle remaining salt mixture evenly over all sides of chicken.

Heat oil in 12-inch skillet over medium-high heat until shimmering. Place chicken breast side up in skillet; transfer to oven; and roast until thickest part of breast registers 150 to 155 degrees, 1 hour to 1 hour 10 minutes, rotating skillet halfway through roasting. Transfer chicken to carving board and let rest for 15 minutes (chicken temperature will continue to rise as it rests).

Meanwhile, pour pan juices into fat separator. Add 2 teaspoons fat to now-empty skillet. Add garlic and cook over medium-low heat, stirring occasionally, until garlic is pale golden brown, about 3 minutes. Add couscous and stir until well combined. Stir in ¼ cup defatted pan juices, water, vinegar, and remaining ½ teaspoon salt and bring to simmer. Spread red peppers in even layer over couscous; turn off heat; cover; and let sit until couscous is just tender and all liquid is absorbed, about 10 minutes.

Carve chicken and transfer to platter. Fluff couscous, stir in basil, season with salt to taste, and transfer to bowl. Serve chicken with couscous.