Step 1Make the crust: Butter a 9-inch springform pan with sides at least 2 3/4 -inches high, and wrap the outside of the pan in a double layer of aluminum foil.
Step 2In a medium bowl, combine the graham cracker crumbs, walnuts, 3 tablespoons sugar and a pinch of salt. Pour in the melted butter and stir together, using your fingers or a fork, until all of the dry ingredients are uniformly moist. Place the crust mixture into the springform pan and use your fingers to pat an even layer (about one-fourth-inch thick) of crumbs over the bottom of the pan and about halfway up the sides. Place the pan in the freezer while you heat the oven.
Step 3Center a rack in the oven and heat the oven to 350 degrees. Place the prepared springform pan on a baking sheet and bake for 10 minutes. Set the crust aside to cool on a rack while you prepare the filling. Reduce the oven temperature to 325 degrees.
Step 4Using a stand mixer or in a large bowl using a hand mixer, beat the cream cheese at medium speed until soft and creamy, about 4 minutes. With the mixer running, add the remaining sugar and one-half teaspoon salt and continue to beat until the cream cheese is light and fluffy, about 4 minutes. Run a spatula along the sides and bottom of the bowl to make sure everything is combined. Beat in the vanilla, then add the eggs one at a time, beating a full minute between each addition -- you want a well-aerated batter. Reduce the mixer to low and beat in the mascarpone. Run a spatula through the batter again to make sure everything is evenly incorporated.
Step 5Place the foil-lined springform pan in a roasting pan. Pour half of the batter into the springform pan. Gently drop the blackberries over the batter, then spoon the remaining batter over the berries and smooth out the top. Make sure that the batter comes no higher than the top of the pan; you might have just a little batter left over.
Step 6Place the roasting pan in the oven and pour enough boiling water to come halfway up the sides of the springform pan.
Step 7Bake the cheesecake for 1 1/2 hours, until the top is browned (and perhaps cracked). Turn off the oven and prop the door open with a wooden spoon. Allow the cheesecake to sit in the water bath for an additional hour.
Step 8Remove the roasting pan from the oven, and remove the springform pan from its water bath. Carefully remove the foil from the springform pan, and cool the cheesecake to room temperature on a rack. Cover the top of the cooled cake lightly with plastic wrap and refrigerate at least 4 hours, preferably overnight.
Step 9To remove the sides of the springform pan: Run a blunt knife around the sides of the pan, then warm the sides of the pan lightly with a hair dryer before unmolding. To slice, run a long, thin knife under hot water then lightly wipe dry. Keep warming the knife as you slice. The cake will keep, tightly wrapped, up to 1 week refrigerated and up to 2 months frozen. (To defrost, place the still-wrapped cheesecake in the refrigerator overnight.)