Preheat oven to 425°F with racks in upper and lower third positions.

Whisk grated garlic, 2 tablespoons oil, 1 teaspoon lemon zest, 1 tablespoon lemon juice, ½ teaspoon mustard, ½ teaspoon salt and ½ teaspoon pepper in a large bowl. Add 1 pound chicken thighs; toss to coat, rubbing the mixture into the chicken.

In a small bowl, combine the remaining 2 tablespoons oil, 1 teaspoon lemon zest, ¼ teaspoon pepper and ¼ teaspoon salt. Toss halved potatoes with half of the oil mixture in a large bowl, then arrange them, cut-sides down, in a single layer on a large rimmed baking sheet (reserve the bowl). Place the chicken on a second baking sheet and arrange the lemon slices around it.

Roast the chicken on the upper rack and the potatoes on the lower rack for 20 minutes. Meanwhile, add 4 cups broccoli to the reserved bowl and toss with the remaining oil mixture.

Remove the potatoes from the oven, flip using a thin metal spatula and arrange the broccoli around them. Roast until the potatoes and broccoli are tender and the chicken is well browned and an instant-read thermometer inserted in the thickest part registers at least 175°F, 10 to 12 minutes.

Sprinkle the chicken, lemon slices, potatoes and broccoli with the remaining ¼ teaspoon salt and divide among 4 plates.

Whisk the remaining 1 tablespoon lemon juice and ½ teaspoon mustard into the pan juices on the chicken baking sheet and drizzle over the chicken and vegetables. Sprinkle with ¼ teaspoon crushed red pepper, if desired.