1 3/4 cups graham cracker crumbs
3 tablespoons light brown sugar
4 tablespoons butter, melted
1 (8-ounce) container mascarpone cheese, softened to room temperature
1 (6-ounce) log goat cheese, softened to room temperature
1 cup ricotta cheese
1 (8-ounce) package cream cheese, softened to room temperature
1-1/4 cup sugar
1 teaspoons pure vanilla extract
1 vanilla bean cut open lengthwise and seeds scraped
Preheat oven to 350 degrees. Stir together the graham cracker crumbs, light brown sugar, and the melted butter. Wrap the outside of a 9-inch springform pan with at least 2 1/2-inch sides in heavy foil. Place the crumbs in the pan and press on the bottom and about halfway up the sides of the pan. Bake for 10 minutes, then set aside on a wire rack to cool.
Reduce heat to 325 degrees. Beat all four cheeses on medium speed with a paddle attachment until soft and creamy. With the mixer running, slowly add the sugar until incorporated, about 3-4 minutes. Beat in the vanilla extract. Beat in the eggs, one by one until all the yellow has disappeared. Beat in the vanilla bean seeds. Pour the batter into the crust.
Place the springform pan in a larger roasting pan where it can sit flat and has some space around it. Pour boiling water into the roasting pan to a depth of about halfway up the sides of the springform pan. (Be careful not to pour water higher than the foil.) Place in oven and bake for 1 hour and 20-30 minutes or until set in the middle and light golden brown. Turn off oven and crack the door open with a wooden spoon and let the cheesecake sit in oven for 30 minutes. Carefully remove from oven and remove the foil from the cheesecake pan and let cool on wire rack to room temperature. Run a knife around edges to loosen the sides. Refrigerate for at least 5 hours or overnight before cutting.