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For the cheesecake: Preheat the oven to 350 degrees F.
Combine the Parmesan, breadcrumbs and butter until thoroughly blended, and press the mixture into the bottom of a 9-inch springform pan.
Heat the oil in a large skillet over high heat. Add the onions and the green and red bell peppers and saute, stirring and shaking the skillet, for 2 minutes. Stir in the corn and the salt and pepper, saute for 1 to 2 minutes 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 5 minutes. Beat in the cream, Gouda, sauteed vegetables and crabmeat. Mix 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. Remove from the oven and allow to cool to room temperature. If you refrigerate the cake, allow it to come to room temperature, for about 1 hour, before serving.
While the cheesecake is cooling, prepare the green onion coulis.
For the green onion coulis: Place the green onions, parsley, shallots and garlic in a food processor or blender and puree. Add the eggs, salt and pepper, and continue to process. With the machine running, stream in the olive oil slowly until it's thoroughly incorporated.
To serve, cut the cake in wedges with a warm knife and serve each wedge with about 3 tablespoons of the coulis.