Preheat oven to 350 degrees and grease the bottom of a 9 inch springform pan. Tip: Wrap the bottom of the pan in foil to prevent leakage.
In a small bowl, combine the brownie mix, 1 egg and water. Using a fork or a whisk, mix thoroughly then spread into the greased pan. Bake for 25 minutes.
Meanwhile, in a heavy saucepan, melt the caramels with the evaporated milk over low heat. Stir often, and heat until a smooth consistency is achieved. Reserve 1/3 cup of the caramel mixture, and pour the remainder over the warm, baked brownie crust.
In a large bowl, beat the cream cheese, sugar and vanilla with an electric mixer until smooth. Add eggs one at a time, beating well after each addition. Pour cream cheese mixture over caramel mixture.
Bake for 40 minutes. Chill in pan at least 4 hours, preferably overnight. When cake is well chilled, loosen by running a knife around the edge, and then remove the rim of the pan. Heat the reserved caramel mixture, and spoon over cheesecake. Drizzle with warmed chocolate fudge topping.