Step 1

Preheat broiler with oven rack 3 to 4 in. from heat. Set a metal cooling rack in a 12- by 17-in. rimmed baking sheet and coat lightly with oil.

Step 2

Remove cooling rack and put squash on baking sheet. Sprinkle with 3 tbsp. oil, 1/4 tsp. salt, and the pepper; toss to coat. Spread squash in a single layer and set cooling rack on top, nudging squash aside as needed so rack lies even.

Step 3

In a large bowl, combine remaining 1/2 tsp. salt with the curry powder, garlic powder, smoked paprika, and cayenne. Set aside 1 1/2 tsp. spice mix.

Step 4

Add remaining 1 tbsp. oil and the chicken thighs to large bowl and toss chicken to coat. Place spiced chicken smooth (skinned) side up on cooling rack over zucchini.

Step 5

Broil chicken and zucchini, turning chicken once, until starting to char at edges, about 16 minutes total.

Step 6

Meanwhile, make glaze: Whisk together reserved spice mix, honey, mustard, and vinegar in a small bowl.

Step 7

Remove chicken and zucchini from oven. Generously brush chicken with glaze. Return to oven and broil, smooth side up, until nicely charred and an instant-read thermometer registers 165° when inserted in thickest part, about 4 minutes. Remove rack of chicken from baking sheet and set aside.

Step 8

Return squash to oven and broil until most pieces are charred, 2 to 3 minutes more. Lift squash from juices and serve with chicken.