How to Make It
Preheat oven to 400°F with an oven rack in center of oven and another oven rack 6 inches from heat.
Toss together squash, zucchini, olive oil, 1/2 teaspoon of the salt, and 1/4 teaspoon of the pepper. Transfer to an aluminum foil-lined rimmed baking sheet, and spread in a single layer.
Microwave pepper jelly in a large microwave-safe bowl on HIGH until melted, about 1 1/2 minutes, stirring every 30 seconds. Whisk in mustard, vinegar, honey, hot sauce, and remaining 3/4 teaspoon salt and 1/4 teaspoon pepper. Remove and reserve 1/4 cup of the pepper jelly mixture.
Add chicken drumsticks to remaining pepper jelly mixture in bowl, and toss to coat. Fit a wire rack over squash on baking sheet; place drumsticks on rack. Bake in center of preheated oven until browned on top, 20 to 25 minutes. Turn drumsticks, and bake until browned on top and a meat thermometer inserted into thickest portion registers 165°F, about 20 minutes. Remove wire rack and drumsticks; brush drumsticks with reserved 1/4 cup pepper jelly mixture.
Increase oven temperature to broil. Transfer baking sheet with squash to upper oven rack, and broil until tender and lightly browned, about 4 minutes. Sprinkle chicken and squash with parsley.