Preheat the oven to 400 degrees. In a large bowl, toss the drumsticks with the olive oil and 1 teaspoon salt. Heat a large skillet over medium-high heat, and brown the drumsticks on all sides, in batches if necessary, about 10 minutes per batch. Transfer to a large shallow roasting pan or rimmed sheet pan.

To the same skillet, add the vegetable oil. When the oil is hot, add the onions, and brown on all sides, about 3 minutes. Add to the roasting pan. Add the peppers and garlic to the skillet, and cook until the peppers are browned on the edges, about 5 minutes. Add the peppers to the roasting pan.

In a spouted measuring cup, stir together the wine, paprika, and remaining teaspoon salt. Pour this into the roasting pan. Roast, uncovered, on the bottom rack of the oven, tossing several times, until the chicken is very tender and glazed with the pan juices, about 40 minutes. Remove the garlic and serve hot.