Preheat the oven to 350ºF.
Combine the Parmesan, bread crumbs, and butter until thoroughly blended, and press the mixture into the bottom of a 9-inch springform pan.
Heat the oil in a medium skillet over high heat. Add the onions and the green and red bell peppers and sauté, stirring and shaking the skillet, for 2 minutes. Stir in the salt and pepper, sauté for 1 minute, and remove from the heat.
Using an electric mixer, beat the cream cheese with the eggs in a large bowl until very thick and frothy, for about 4 minutes. Beat in the cream, Gouda, the sautéed vegetables, and the smoked salmon, and beat until thoroughly incorporated and creamy, for about 2 minutes.
Pour the filling over the crust in the springform pan and bake until firm, for about 1 hour 15 minutes. Allow to cool to room temperature; if you refrigerate the cheesecake before serving, remove from the refrigerator and allow to come to room temperature, for about 1 hour.
Prepare the Green Onion Coulis
To serve, cut in wedges with a warm with a warm knife and serve each wedge with 2 or 3 tablespoons of the Green Onion Coulis.
Yield: 12 to 16 brunch servings
Note: Remove the crusts from a dense, homemade-type white bread, and crumb 3 or 4 slices at a time in a food processor or blender. Store in an airtight container at room temperature for up to 3 days.