Melt butter in a large skillet over medium heat. Add onion and garlic; cook and stir until onion is translucent, about 5 minutes. Stir in chili powder and cumin; cook and stir until fragrant, about 2 minutes. Add sausage; cook, stirring to break up clumps, until juices run clear, 5 to 8 minutes.
Stir kidney beans and mushrooms into the skillet. Cook until heated through, about 5 minutes. Mix in pumpkin until warm, about 2 minutes. Pour in milk. Simmer until flavors combine, about 10 minutes. Season with salt; scatter Cheddar cheese on top.