Grate 1 cup cheddar cheese, set aside.
Wash and slice 3 cups mixed mushrooms, thinly slice 2 shallots, finely chop 1 tsp. thyme and remove 1 tsp. thyme leaves from stems.
Sauté mushrooms, without moving them, in 2 tbsp. olive oil until brown for 7-8 minutes. Once seared on one side, stir and sauté for 3 minutes more. Once seared, add sage and thyme. Sauté for 1-2 minutes longer, and remove from the pan.
Add 1 tbsp. olive oil to the pan with sliced shallots. Brown for 3-4 minutes, then add ½ cup loose sausage to the pan. Sauté until brown. About 3-4 more minutes.
Add mushrooms and herbs back to the pan with shallots and sausage. Season with ⅛ tsp. chili pepper, ⅛ tsp. smoked paprika, a sprinkle of salt and pepper. Sauté for 1 minute more. Turn off heat under mushrooms, leave them in the pan to stay warm.
Bring 4 cups vegetable broth to a simmer (first, check your polenta box to make sure if you should use 4 or 3 cups), slowly add 1 cup polenta while stirring. Once it appears to be setting (it should quickly), add ½ cup pumpkin purée, 1 cup grated cheddar, and ½ tsp. salt. Cover with a lid, heat the mushrooms and sausage for a minute or 2 if they’re no longer warm. Pour polenta into a bowl, and top with mushrooms.