Toss fennel and 2 teaspoons oil in a 9-by-13-inch baking dish. Bake for 10 minutes.
Meanwhile, place rosemary, lemon zest, garlic, pepper and salt together on a cutting board. Rock a chef's knife through the ingredients until they are minced into a fine paste. Transfer the paste to a small bowl and combine with 1 teaspoon oil. Rub the paste all over drumsticks.
Heat the remaining 2 teaspoons oil in a large nonstick skillet over medium-high heat. Add the drumsticks; cook, turning occasionally, until browned on all sides, 4 to 5 minutes.
After the fennel has roasted for 10 minutes, stir in pine nuts and place the browned drumsticks on top of the fennel. Return to the oven and bake until the fennel is golden and an instant-read thermometer inserted into the thickest part of a drumstick without touching the bone registers 165 °F, 15 to 20 minutes more. Remove the chicken from the pan. Toss the fennel with vinegar in the baking dish, scraping up any browned bits. Serve the fennel with the chicken.