Lightly butter an 8 inch springform pan. Mix 2 tablespoons Parmesan cheese with the breadcrumbs. Sprinkle this mixture into the pan; turn and tap pan to coat inside of pan. Wrap a large piece of foil underneath and up the sides of the pan. Be careful not to tear any holes in the foil.
In a medium skillet or frying pan, melt butter over medium heat. Add onions and green peppers and saute until tender, about 5 minutes. Remove from heat and let cool slightly.
In a large bowl, beat together cream cheese, eggs and cream until well blended. Fold in onions, peppers, salmon, Swiss cheese, 3 tablespoons Parmesan cheese, salt and pepper. Pour into prepared pan.
Place the wrapped springform pan inside a large roasting pan. Place the pans in the oven and pour enough boiling water into the outside pan to come 2 inches up the side of the springform pan.
Bake until firm to the touch, about 1 hour and 40 minutes. Carefully remove both pans from the oven and turn off the heat. Lift springform pan out of the water and return it to the oven. Let stand in the cooling oven for 1 hour. Transfer to a wire rack and let cool completely.