Using a paper towel or your fingertips, generously butter the inside of the springform pan. Use a double layer of heavy-duty aluminum foil to wrap tightly around the bottom of the pan. This prevents any water from the water bath seeping into the pan.
In the work bowl of a food processor fitted with the steel blade, combine the cookies, walnuts, and sugar and pulse until the cookies are finely ground, about 2 minutes. Or place the cookies in a sturdy plastic bag and seal it. Use a rolling pin to crush the cookies to a very fine crumb consistency. Finely chop the walnuts and add them with the sugar to the cookies, seal the bag, and shake to blend together evenly.
Transfer the cookie crumb mixture to a medium bowl and add the butter. Use a rubber spatula or a spoon to toss the mixture together to moisten all of the cookie crumbs.
Transfer the crust to the prepared springform pan and use your fingertips to press it into the bottom and partway up the sides of the pan. Chill the crust while preparing the cheesecake batter.
Place the milk chocolate in the top of a double boiler over low heat. Stir often with a rubber spatula to help melt evenly. Remove the top pan of the double boiler and wipe the bottom and sides very dry.
Or place the milk chocolate in a microwave-safe bowl and melt on low power for 30-second bursts. Stir with a rubber spatula after each burst.
Place the cream in a small saucepan and bring to a boil over medium heat. Turn off the heat, add the malted milk powder, and whisk to distribute evenly. Cover the pan and let the mixture steep for 10 minutes, then strain the cream.
Place the cream cheese in the bowl of an electric stand mixer or in a large bowl. Use the flat beater attachment or a hand-held mixer to beat the cream cheese on medium speed until it's fluffy, about 2 minutes.
Add the sugar and cream together very well. Stop occasionally and scrape down the sides and bottom of the bowl with a rubber spatula.
One at a time, add the eggs to the cream cheese mixture, beating well after each addition. At first the eggs will sit on top of the cream cheese mixture, but stop often to scrape down the sides and bottom of the mixing bowl with a rubber spatula. This will help the mixture to blend. The mixture may also look curdled as the eggs are added, but as you stop and scrape down the bowl, the mixture will smooth out.
Add the sour cream and vanilla to the cream cheese mixture and stir together to combine.
Add the strained cream to the batter and blend thoroughly, then add the melted milk chocolate and mix together.
Transfer the batter into the crust in the springform pan. Use a rubber spatula to smooth and even the top.
Place the springform pan in the larger cake pan or roasting pan and set the pan on the oven rack. Carefully pour the boiling water into the bottom pan until it reaches halfway up the side of the springform pan. Baking the cake in a water bath cushions it from the heat and adds extra moisture to the oven, which keeps the top of the cake from cracking.
Bake the cake for 1 hour and 45 minutes, until the top is set, but jiggles slightly. Remove the pan from the oven and transfer the cheesecake to a rack.
Remove the foil and let the cheesecake cool completely. Cover the top of the cheesecake with waxed paper and wrap the pan tightly with aluminum foil. Refrigerate the cake for at least 6 hours before serving. To unmold the cheesecake, dip a thin-bladed knife in hot water and dry, then run it around the inner edge of the pan. Release the clip on the rim of the pan and gently lift it off the cake.
Store the cheesecake, covered with waxed paper and tightly wrapped with aluminum foil, in the refrigerator up to 4 days. To freeze up to 2 months, wrap the cake pan tightly in several layers of plastic wrap and aluminum foil. Use a large piece of masking tape and an indelible marker to label and date the contents. If frozen, defrost overnight in the refrigerator and bring to room temperature at least 30 minutes before serving.