Preheat oven to 350°F. Grease a 1 ½ qt casserole dish.
Place bread cubes in the prepared dish and sprinkle raisins evenly over the top.
In a bowl, whisk together eggs, heavy cream, milk, pumpkin puree, cooled melted butter, brown sugar, and pumpkin pie spice until smooth.
Pour the custard mixture over the bread, pressing lightly so it soaks up the liquid.
Refrigerate for 30 minutes to 1 hour (longer gives a thicker texture).
Cover with foil and bake for 20 minutes. Remove foil and bake another 40 minutes, until golden on top and set in the center.
Let cool 5–10 minutes. Drizzle the caramel over the top before serving.