Step 1Heat the oven to 325 degrees. Wrap the outside of an 8-inch springform pan with foil and set aside.
Step 2Combine the cream cheese, goat cheese, sugar and vanilla pulp in the bowl of an electric mixer and beat until smooth and creamy. Add the mascarpone and beat until smooth.
Step 3Add the eggs and mix well, scraping down the sides of the bowl with a rubber spatula as necessary. Strain the mixture into a bowl.
Step 4Spoon the mixture into the pan and place it in the center of a larger baking pan. Pour enough very hot water into the baking pan to reach two-thirds of the way up the side of the springform pan. Cover the entire baking dish with foil. Pierce the foil in several places with a knife. Bake the cake for 1 hour, then lift off a corner of the foil to allow the steam to escape. Recover the pan and bake until the cake looks rather wet and is still very slightly jiggly in the center, but the edges are set, 40 to 45 minutes longer.
Step 5Transfer the cake to a wire rack to cool completely before serving. The cake can be made up to 2 days ahead and kept covered in the refrigerator.