In a medium saucepan combine blackberries, the 3 tablespoons sugar, the cornstarch, and water. Cook and stir until thickened and bubbly. Cook and stir 2 minutes more. Press mixture through a fine sieve; discard seeds. Stir in blackberry brandy or rum and 1/2 teaspoon orange peel. Cover and chill sauce.
For filling, in large mixing bowl beat cream cheese, the 1 cup sugar, the flour, and vanilla with an electric mixer on medium to high speed until combined. Add eggs and egg yolk all at once. Beat on low speed just until combined. Stir in milk and orange peel.
Pour half of filling into crust-lined springform pan. Drizzle half of blackberry mixture on top. Repeat with remaining filling and sauce. Use a spatula to gently swirl the filling and sauce.
Bake cheesecake on a shallow baking pan in a 375 degree F oven for 50 to 55 minutes or until center of cheesecake appears nearly set. Cool cheesecake in springform pan on a wire rack for 15 minutes. Using a small metal spatula, loosen crust from the sides of the pan. Cool for 30 minutes more. Remove the sides of the springform pan. Cool the cheesecake completely, then chill for at least 4 hours. Makes 12 to 16 servings.