Pat the drumsticks completely dry and place on a baking sheet fitted with a cooling rack. Mix 1/4 cup salt, a few grinds black pepper and the sugar in a small bowl, then rub the mixture all over the drumsticks. Refrigerate, uncovered, for 4 hours and up to overnight. Rinse the legs and pat them completely dry.
Preheat the oven to 350 degrees F.
Mix the butter with the cumin, thyme, 1/2 teaspoon salt and a few grinds of black pepper and rub the mixture all over the drumsticks, getting underneath the skin if you can. Brush the drumsticks all over with the pomegranate molasses. Add 1 cup water to the bottom of the baking sheet and tent the sheet with foil. Bake for 1 hour and 30 minutes.
Remove the foil from the pan and brush the turkey legs all over with the pomegranate molasses. Continue baking for 30 minutes, uncovered, then brush one last time. Bake until the skin is crispy and the turkey has reached 165 degrees F (avoiding bone), about 30 minutes more. Brush a final time with the molasses (be sure to use a fresh bowl of molasses and a clean brush to avoid cross-contamination with raw turkey juices) and let rest for 10 minutes. Slice the turkey and serve with the remaining pomegranate molasses on the side.