1. Preheat the oven to 350°. On a rimmed baking sheet, toss the brioche with the melted butter and bake for 20 minutes, or until golden and crisp. Let cool.
2. Melt the remaining 2 tablespoons butter in a large skillet. Add the leeks and garlic and season with salt and pepper. Cover and cook over moderate heat for 5 minutes, then uncover and cook, stirring, until softened, about 5 minutes longer. Add the wine and cook until evaporated, then remove from the heat and stir in the parsley and thyme;let cool.
3. In a large bowl, whisk the eggs with the milk, cream and stock. Add the leek mixture and season generously with salt and pepper. Stir in the brioche and cheese. Transfer the mixture to a 3- to 4-quart buttered baking dish. Cover with plastic and refrigerate overnight. Bring to room temperature before baking.
4. Preheat the oven to 375°. Toss the bread to make sure it's evenly soaked. Cover with a buttered sheet of foil and bake for 1 hour, or until just set. Remove the foil and bake for 30 minutes longer, or until the top is golden and crisp.
Make Ahead: The bread pudding can be refrigerated overnight. Cover the baking dish with foil and reheat in a 350° oven; uncover and recrisp under a broiler.