Make the polenta. Combine 1 cup polenta, 3¼ cups chicken stock, and ½ tsp Kosher salt in a medium saucepan, then bring liquid to a boil. Reduce the heat to medium-low, then stir occasionally until thick and creamy, about 20 minutes.
Flavor the polenta. Whisk in ¾ cup canned pumpkin, ½ cup grated Parm, 3 Tbsp butter, 1 large egg, 2 Tbsp chopped rosemary (or other fresh herb), remaining ½ tsp Kosher salt, and ¼ tsp black pepper until very well mixed and butter and cheese has melted. Remove from the heat and set aside.
Cook the pancetta. In a medium skillet, heat 1 Tbsp neutral oil over medium-high heat. When hot, add pancetta, then cook until crispy on all sides, about 3-5 minutes, stirring occasionally. Use a slotted spoon to drain onto a paper towel lined plate.
Sauté the Swiss chard. Heat the same skillet over medium-high and drain off all but 2 tsp of grease. Add the chard stems and cook, stirring occasionally, for 3–4 minutes. Add the shallot and cook 3–4 minutes more, then stir in the chard leaves and garlic. Season with ½ tsp kosher salt and cook until wilted, about 2–3 minutes. Finish with the juice of ½ lemon, stir, and taste.
Assemble, then serve! If needed, reheat the polenta over medium heat, stirring to loosen and adding a splash of stock or cream as needed. Transfer to a serving bowl, top with the sautéed Swiss chard, then garnish with crispy pancetta and fried sage. Finish with extra grated Parmesan and serve warm.