Clean the chicken drumsticks, then season with salt and pepper. Rub with crushed garlic and place fresh rosemary on top. Let it stand for 15 minutes.
Heat olive oil in a large skillet over medium-high heat. Sear the chicken drumsticks on both sides until golden brown.
Transfer the chicken drumsticks to a baking sheet, drizzle with the remaining oil from the skillet, and bake in a preheated oven at 350°F (180°C) for 40 minutes, or until fully cooked through.
Meanwhile, prepare the steamed vegetables: melt butter in a large saucepan, then steam the chopped carrots, green peas, and broccoli. Add a pinch of salt and a squeeze of lemon juice.
Once the chicken drumsticks are cooked, serve them with the steamed vegetables. Garnish with fresh herbs, if desired.
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