Preheat oven to 350 degrees F.
In a large saute pan, saute sausages, and place in the oven at 350 degrees for about 7 to 8 minutes. Lower oven temperature to 250 degrees F.
Meanwhile, start the polenta. Combine milk, stock, chile, butter, herbs, salt, and pepper in a heavy saucepan. Bring to a boil and remove herbs. Slowly pour in polenta whisking constantly until thick. Remove immediately and add the cheese, stirring until incorporated. Pour into a lightly buttered bowl. Place in 250 degree F oven until ready to serve.
Remove sausage from the pan and drain the fat. To the same pan, add shallots, garlic, and mushrooms. Cook until soft. Add wine and tomatoes and place sausages back into the pan. Reduce down 3/4 of the way; finish with picked basil and butter. Remove polenta from oven, invert onto a large platter. Place sausage mixture around the polenta.