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. Stir or whisk in ¾ cup canned pumpkin purée, ½ cup grated Parmesan, 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 or bowl.
Sauté the Swiss chard. Heat the same skillet over medium-high heat. Drain off all but 2 teaspoons of grease. When hot, add the Swiss Chard stems. Cook for 3-4 minutes, stirring occasionally, then add the thinly sliced shallot. Cook an additional 3-4 minutes, then add the chopped Swiss chard leaves and thinly sliced garlic. Season with ½ tsp Kosher salt, then cook until the Swiss chard has wilted and cooked down, and the garlic is a light golden brown, about 2-3 minutes more. Squeeze the juice of half a lemon on top, stir, then taste and adjust seasoning, as needed.
Assemble, then serve! If needed, reheat the polenta over medium heat and stir to loosen. You can add a splash of stock or heavy cream (if using) as needed. Pour into a large serving bowl. Add the sautéed Swiss chard on top, then garnish with crispy pancetta and sage leaves. Optional garnish: sprinkle with a little extra grated Parmesan. Serve immediately!