01 - 
                Pour vegetable broth into a medium saucepan and bring to a gentle simmer over medium heat.
              
              
              
                02 - 
                Gradually whisk in yellow cornmeal to the hot broth, stirring constantly to prevent lumps. Reduce heat to low and continue stirring for 10–15 minutes until the mixture thickens and pulls away from the pan sides.
              
              
              
                03 - 
                Stir pumpkin puree, salt, black pepper, and nutmeg into the thickened polenta. If using, fold in grated Parmesan cheese. Cook for 5 minutes, ensuring all ingredients are fully combined.
              
              
              
                04 - 
                Meanwhile, melt unsalted butter in a small skillet over medium heat. Add fresh sage leaves and cook, swirling occasionally, until the butter turns golden brown and sage leaves are crisp, about 3–4 minutes. Avoid burning the butter by lowering the heat as needed.
              
              
              
                05 - 
                Ladle the hot pumpkin polenta into warm bowls. Spoon the browned sage butter and crispy sage leaves over the top. Finish with a generous drizzle of olive oil. Optionally, garnish with extra Parmesan or toasted pumpkin seeds.