Start by prepping the ingredients: slice all the vegetables, open cans, and peel garlic. Set aside.
Combine flour, salt, and pepper in a large zip-lock bag and mix it together. Place chicken drumsticks into the bag with flour, close the bag, and shake it up to coat all the drumsticks evenly with flour mixture.
Take drumsticks out and gently shake off excess flour if needed. (Discard remaining flour and the bag.)
Preheat a large, oven-safe baking pan over medium heat. Add olive oil and chicken drumsticks. Sear drumsticks for just a few minutes on each side, until golden brown and take chicken out of the pan. Set them aside on a separate dish.
Add onions and peppers to the pan and cook until softened. Smash and mince garlic and add it to the pan with veggies. Add mushrooms and cook until garlic is fragrant.
Pour in wine and let it simmer for a few minutes.
Preheat oven to 375°.
Add tomatoes, capers, sliced olives, tomato paste, and chicken broth and carefully stir everything together. Season with salt, pepper, oregano, and basil and mix until everything is evenly incorporated.
Nestle chicken back into the pan among all the vegetables and sauce and transfer the pan into the oven.
Bake for about 35 minutes, until chicken is fully done.