Preheat oven to 400°F with rack in middle and generously butter a 13- by 9-inch shallow baking dish or pan (3-quart; preferably glass or ceramic).
Arrange bread in 1 layer in baking dish. Dissolve espresso powder in hot water in a large bowl. Whisk in milk, eggs, vanilla, and 1/2 cup sugar until smooth.
Pour custard over bread, then turn slices over several times so they soak up as much custard as possible. Sprinkle top with remaining 2 tablespoons sugar.
Bake until puffed and set, 20 to 25 minutes. Cool in dish on a rack 10 minutes, then dust with cinnamon.