Preheat oven to 275°F (135°C). Season turkey legs generously with salt and pepper on all sides.

Heat oil in a large straight-sided sauté pan over high heat until shimmering. Add turkey legs, skin side down. Cook, without moving, until turkey is deep golden brown, about 8 minutes. Flip legs and cook until second side is browned, about 5 minutes longer, reducing heat as necessary if oil smokes excessively. Transfer turkey to a large plate.

Return sauté pan to heat and add onion, carrot, celery, garlic, thyme, and rosemary. Cook, stirring frequently, until vegetables are well browned, about 8 minutes total.

Add wine, bring to a boil, and cook until reduced by half, about 5 minutes. Add stock and bay leaves and bring to a boil. Nestle turkey legs into pan, letting them rest on the vegetables so that only their skin is exposed.

Transfer to oven and cook, uncovered, until legs are fall-apart tender, sauce is reduced, and skin is deep mahogany, about 2 hours. Carefully remove from oven and transfer turkey legs to a plate using a slotted spatula.

Strain liquid through a fine-mesh strainer into a large bowl or medium saucepan. Discard solids. Skim excess fat from surface and discard. Set liquid aside.

In a large saucepan over medium-high heat, melt butter. Add flour and cook, whisking constantly, until golden brown, about 2 minutes. Slowly whisk in hot turkey-cooking liquid until fully incorporated. Bring to a boil to thicken and season to taste with salt and pepper.

Carve each turkey leg between the thigh and the drumstick, removing thigh bone if desired. Transfer to a serving platter. Sprinkle with chives and serve with hot gravy.