Preheat your oven to 425°F. Pat the drumsticks dry with paper towels and add them to a bowl. Add the cooking oil, garlic powder, onion powder, paprika, salt, black pepper, Cajun seasoning, and thyme. Get in there and make sure every drumstick is coated.
Arrange the drumsticks on a lined sheet pan with a little room between each piece. Bake at 425°F for 35–45 minutes, flipping them about halfway through.
Peel the potatoes if you'd like and cut them into evenly sized chunks. Place them in a pot of cold, salted water. Bring to a boil and cook for approximately 15–20 minutes, until they're completely fork-tender. Drain thoroughly.
Melt 4 tablespoons butter over low heat. Add your minced garlic and cook for about 30–45 seconds. Add ½ cup milk or half-and-half and gently warm the mixture.
Pour the warm garlic-butter mixture into the potatoes. Mash until creamy. Season with salt and black pepper to taste.
Melt 2 tablespoons butter in a skillet over medium heat. Add your sliced onions. Cook for approximately 5–7 minutes, stirring occasionally, until they're softened and lightly golden.
Sprinkle 2 tablespoons flour over the butter and onions. Stir everything together and cook for approximately 1–2 minutes.
Slowly pour in 2 cups chicken broth, whisking as you go.
Whisk in ½ cup milk or half-and-half, Worcestershire sauce, garlic powder, onion powder, and black pepper. Bring everything to a gentle simmer.
Place the cooked drumsticks directly into the gravy. Spoon some of that onion gravy over the top. Let everything gently simmer together for about 3–5 minutes.
Add a generous mound of garlic mashed potatoes to your plate. Place 2–3 drumsticks alongside or slightly over the potatoes. Spoon that onion gravy over the chicken and potatoes.
