Step 1: Preheat Oven: Preheat the oven to 400F (200C).
Step 2: Prepare Vegetables: In a large bowl, combine the quartered potatoes, onion wedges, sliced carrots, and broccoli florets.
Step 3: Season Vegetables: Drizzle the vegetables with olive oil, then add minced garlic, salt, and pepper. Toss to coat evenly.
Step 4: Arrange on Baking Sheet: Spread the seasoned vegetables in a single layer on a large baking sheet.
Step 5: Season Drumsticks: In a separate bowl, pat the chicken drumsticks dry with paper towels. Season them generously with dried rosemary, dried thyme, paprika, salt, and pepper.
Step 6: Add Drumsticks to Baking Sheet: Arrange the seasoned drumsticks among the vegetables on the baking sheet, ensuring they are not overcrowded.
Step 7: Bake: Bake in the preheated oven for 40 minutes, or until the chicken is cooked through and the juices run clear when pierced with a fork, and the vegetables are tender and slightly browned.
Step 8: Rest: Let the dish rest for 5 minutes before serving. This allows the juices to redistribute within the chicken.
Tip: For extra crispy chicken skin, broil for the last few minutes, watching carefully to prevent burning. Substitute other vegetables based on preference, such as bell peppers, zucchini, or sweet potatoes.