1. Preheat oven to 400°. Heat 2 tablespoons oil in a large skillet over medium-high heat. Sprinkle leeks with 1/2 teaspoon kosher salt and 1/4 teaspoon pepper. Sauté leeks, in 2 batches, adding 2 tablespoons oil to pan between batches. Place sautéed leeks, cut sides up, in a 13- x 9-inch baking dish.
2. Add remaining 1/4 cup oil to skillet; heat over medium heat. Add shallots, thyme, remaining 1/2 teaspoon kosher salt, and remaining 1/4 teaspoon pepper. Cook about 4 minutes or until shallots are tender.
3. Stir in wine, increase heat to medium-high, and cook until reduced by half. Stir in stock, and bring to a boil. Remove from heat, and pour mixture over leeks. Bake 30 minutes or until leeks are tender when pierced with a fork.