Coat a 1 1/2- to 2-quart shallow baking dish with cooking spray.
Simmer coffee in a saucepan over low heat until it is reduced to 1/2 cup, 7 to 8 minutes; let cool to lukewarm.
Whisk together eggs, brown sugar and cinnamon in a mixing bowl until smooth. Whisk in 1 1/2 cups evaporated milk, then add the lukewarm coffee.
Arrange bread cubes in an even layer in the prepared baking dish. Pour the milk mixture evenly over the bread. Let soak for 30 minutes. Meanwhile, preheat oven to 325 °F.
Sprinkle almonds over the top of the pudding and bake for 25 minutes. Increase oven temperature to 425 ° and bake until the top is browned and the nuts are toasted, 5 to 8 minutes longer. Let stand for 10 minutes before serving with sauce.
To make the sauce: Combine granulated sugar, lemon juice and water in a small heavy saucepan. Bring to a boil over medium-high heat, stirring occasionally. Cook, without stirring, until the syrup turns deep amber, 10 to 15 minutes. Remove the caramel from the heat and let cool for 2 minutes. Whisk in butter until it is incorporated, then gradually whisk in 3/4 cup evaporated milk. Return to low heat and stir until the caramel has dissolved completely. Whisk in vanilla. Let cool slightly before serving.
Dust the top of the pudding with confectioners' sugar and serve with the caramel sauce.