How to Make It
Preheat oven to 325°F with racks in middle and lower third positions. Place milk and peppercorns in a large saucepan; bring milk just to a boil over medium-high. Remove from heat; let steep 30 minutes. Pour through a fine-mesh strainer into a bowl; discard solids.
Whisk together eggs, egg yolks, salt, 1/2 cup of the granulated sugar, and 1/4 teaspoon of the cardamom in a separate large bowl until smooth. Slowly pour strained milk into egg mixture, whisking constantly until combined. Set aside until ready to use.
Stir together softened butter and remaining 2 tablespoons granulated sugar and 1/2 teaspoon cardamom in a small bowl until combined. Spread mixture evenly over both sides of bread slices (it’s OK if bread isn’t completely covered in butter). Arrange bread slices evenly on 2 rimmed baking sheets. Bake in preheated oven until bread is dry to the touch and golden brown, about 20 minutes, flipping bread slices and rotating baking sheets between top and bottom racks halfway through cook time. Remove from oven.
Cut toasted bread slices in half. Grease a 13-x 9-inch broiler-safe baking dish with softened butter. Arrange bread slices, slightly overlapping, in prepared baking dish. Pour egg-milk mixture over bread; press bread into liquid until completely moistened. Cover and chill at least 8 hours (or up to 12 hours).
Preheat oven to 325°F. Meanwhile, uncover bread mixture; let stand at room temperature 30 minutes.
Brush top of bread mixture in dish evenly with melted butter; sprinkle with pearl sugar. Bake until just set (center should have the texture of bread pudding), about 20 minutes. Set oven to broil. (If oven does not have a separate broiler, there’s no need to remove dish from oven.) Broil French toast until top is golden in spots, about 2 minutes. Remove from oven; let cool 5 minutes. Serve French toast with maple syrup.