Pat drumsticks dry with paper towels. In a small bowl, combine olive oil, minced garlic, paprika, garlic powder, onion powder, Italian seasoning, salt, and black pepper to make an herb paste. Rub the mixture generously over each drumstick, coating all sides. Arrange on a baking sheet lined with foil in a single layer.

In a medium pot, melt butter over medium heat. Add rice and stir for about 1 minute to toast the grains. Pour in chicken broth and add salt to taste. Bring to a boil, then reduce heat to low, cover, and simmer for 15-18 minutes until liquid is absorbed. Let sit covered for a few minutes before fluffing.

Preheat oven to 400 degrees Fahrenheit. Once hot, place drumsticks in the oven and roast for 25-30 minutes, rotating the pan halfway through. Chicken is done when the skin is deeply golden and caramelized, and a meat thermometer inserted into the thickest part reads 165 degrees Fahrenheit.

About 15 minutes before the chicken is done, melt butter in a separate pan or on a section of the baking sheet. Toss broccoli florets with the melted butter, minced garlic, salt, and black pepper. Cook over medium-high heat for 12-15 minutes, stirring occasionally, until tender with charred edges. Alternatively, roast on a baking sheet alongside the chicken at 400 degrees.

Arrange cooked rice as a base on a plate, nestle golden drumsticks on top, and add roasted broccoli to the side. Sprinkle fresh parsley generously over the chicken and rice. Serve hot.