Preheat your oven to 350°F (175°C). Lightly grease a 9x13-inch (23x33 cm) baking dish.
Spread the bread cubes in an even layer in the prepared dish.
In a large bowl, whisk the eggs lightly. Add the pumpkin purée, half-and-half, milk, granulated sugar, brown sugar, vanilla, cinnamon, ginger, nutmeg, cloves, and salt. Whisk until the mixture is smooth and well combined.
Pour the pumpkin custard evenly over the bread cubes. Use a spoon to gently press the bread down, ensuring it is all coated in the liquid.
Let the dish stand at room temperature for 30 minutes. This allows the bread to soak up the custard.
Bake for 45 to 55 minutes. The pudding is done when the center is set and a knife inserted near the middle comes out clean. The top should be golden brown.
For safety, ensure the internal temperature of the custard reaches at least 160°F (71°C) on an instant-read thermometer.
Remove from the oven and let the bread pudding cool on a wire rack for at least 15 minutes before serving.