Preheat the oven to 350 degrees . Line a 12-cup muffin tin with paper or foil liners.
In a medium skillet, melt the butter with the brown sugar over moderately high heat. Add the pumpkin cubes and 1 tablespoon of water and cook, covered, for 10 minutes, stirring occasionally, until the pumpkin is softened and caramelized. Remove from the heat and let cool.
In a large bowl, whisk together the milk, eggs, vanilla, cinnamon, ginger and nutmeg.
Stack the toasted bread, slice off the crusts and cut the bread into 4 triangles.
Add the bread to the custard and let soak until the custard is absorbed, about 10 minutes. Stir in the cooled caramelized pumpkin and the chocolate.
Spoon the mixture into the prepared muffin cups (they'll be full). Bake the puddings until puffy and golden, about 25 minutes.