Preheat the oven to 325 degrees F. and grease a 9 inch springform pan and line it with parchment paper. Wrap the bottom of the springform pan with foil so no batter leaks out and place it on a baking sheet. Put the cubes of rugelach into the pan and set it aside.
In a stand mixer, beat the cream cheese, sour cream and sugar until light and fluffy. Add the vanilla extract and salt and mix until combined. With the mixer on low, add the eggs, one at a time, until all 3 eggs are incorporated into the batter. Lastly, add the milk and mix on low until combined. Scrape down the sides of the bowl to make sure all of the cream cheese and sour cream is combined with the milk.
Pour the batter over the rugelach and set it aside to soak for 30 minutes.
Bake the bread pudding cheesecake for 1 hour 15 minutes, until the edges have set and the center is still a bit wiggly. Turn off the oven, prop open the door and leave the cheesecake inside the oven for 2 hours to cool. This will keep the cake from cracking too much on top.