Put the broth, pumpkin puree, cumin, cinnamon, salt, pepper, and cayenne (if using) into a large saucepan.
Set over medium-high heat; whisk occasionally until the pumpkin dissolves and the mixture comes to a simmer.
Reduce the heat to medium-low. Whisk in the polenta.
Continue stirring until thick and creamy, about 3 minutes. Serve and enjoy!