Heat 1/2 cup oil in a pan over medium-high heat and season prepared leeks with salt and pepper to taste. Place leeks cut side down in the pan and sear until golden brown, 4-5 minutes. Season again with salt and pepper and flip, allowing to cook for an additional 3 minutes. Transfer leeks to a baking dish.
Preheat oven to 400 degrees. Add the remaining 2 tablespoons of oil to the pan; add shallots, garlic, thyme, lemon zest, and a little salt and pepper. Allow to cook until just brown, about 5 minutes. Add wine and cook until reduced by half, 8-10 minutes. Add stock and bring mixture to a boil.
Pour stock mixture over leeks until they are almost but not quite submerged. Put in the oven and allow to braise until tender, about 30 minutes.
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