Leek and Gruyere Bread Pudding

Name: Leek and Gruyere Bread Pudding
Ingredients: 3 tablespoons unsalted butter, plus more for baking dish; 1 bunch leeks (4 or 5), white and pale-green parts only, thinly sliced crosswise, rinsed well; 2 garlic cloves, crushed; ⅓ cup dry white wine; 3 cups heavy cream; 2 cups whole milk; ½ teaspoon freshly grated nutmeg; Pinch of cayenne pepper; 2 teaspoons coarse salt; ¼ teaspoon freshly ground pepper; 5 large eggs plus 2 large egg yolks, lightly beaten; 1 loaf day-old brioche (about 1 pound), crusts removed, cut into ¾-inch slices and then halved crosswise; 2 cups grated Gruyere cheese; 1 cup grated Parmesan cheese