Bring brine ingredients to a boil to dissolve salt. Add ice and cool.
Pour into double-bagged 2-gallon plastic baggies, add turkey legs and let the legs brine for 1-2 days.
To cook, heat a large, wide, oven-safe braising pan or large, deep, cast-iron skillet over medium-high heat with olive oil, about 3 turns of the pan. Remove turkey legs from brine, pat them dry and season with salt and pepper. Add legs to the pan and brown 8-10 minutes on one side then turn and brown 5-6 minutes more; remove to platter.
Add another turn of the pan of olive oil along with the vegetables, juniper and allspice berries, peppercorns and herbs. Season with salt and cook to soften, 8-10 minutes. Add wine to pan and ruduce by 2/3, about 6-7 minutes. Add stock and turkey legs back into pan, keeping top half of turkey exposed. Transfer pan to oven and roast 2 hours uncovered, spooning pan sauce over the legs occasionally.
Remove legs to platter and cover. Strain sauce then place pan over medium-high. Add butter and melt, then whisk in flour. Add strained sauce to pan and cook to thicken gravy.
Serve turkey legs topped with gravy with Brown Butter Polenta alongside.
