Saute about 1/4 of the mushrooms in butter over high heat until browned. Add shallots, reduce heat to keep from burning, and continue sauteing until soft. Add garlic and saute for 1 minute more. Add peas and salami, and season, to taste, with salt and pepper. Set aside in a sealed plastic container to keep warm. Reserve pot for polenta.
Bring water to a boil, then slowly stir in cornmeal with a fork. Reduce heat as low as possible. Continue to cook for 5 to 10 minutes, stirring often. Turn heat off and add cheese and butter, and season, to taste, with salt and pepper. Top with ragout and serve.