Heat oven to 350 degrees.
Combine Parmesan, bread crumbs and butter in a small bowl; press mixture over bottom of a 9-inch springform pan.
Heat oil in a medium skillet over high heat. Add the onions and the green and red peppers and sauté, stirring and shaking skillet for 2 minutes. Stir in salt and pepper, sauté for 1 minute and remove from heat.
Beat together cream cheese and eggs with an electric mixer in a large bowl until very thick and frothy, about 4 minutes. Beat in cream, Gouda, sautéed vegetables and smoked salmon until thoroughly incorporated and creamy, about 2 minutes.
Pour filling over crust and bake until firm, about 1 hour 15 minutes. Let cool to room temperature. Refrigerate at least 6 hours or overnight.
Remove cheesecake from refrigerator about 1 hour before serving. To serve, cut cheesecake in wedges with a warm knife.
Yield: 12 to 16 servings