Make the crust: Heat oven to 300ºF.
Melt the butter in a 3-quart saucier over medium-low heat. Brush a 9-by-3-inch round cake pan with some of the melted butter and line with parchment paper.
In a food processor, process the graham crackers with the sugar, being sure to leave some larger pieces. Drizzle in the rest of the melted butter and pulse to combine.
Dump two-thirds of the crumb mixture into the bottom of the parchment-lined cake pan and tap into place with the bottom of a water glass. When your floor of crumbs is well packed, add the last third of the crumbs to the pan, then move the glass in a circular motion to push the crumbs up the side of the pan forming a wall 1 1/2 inches high. As the wall forms, begin rolling the glass around the inside of the pan to pack the wall into place.
Bake for 15 minutes, then cool for 10 minutes before filling. Reduce oven temperature to 250ºF.
Make the filling: Bring 2 quarts water to a boil in an electric kettle.
Combine the vanilla, eggs, egg yolks, and cream in a small bowl and set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the cream cheese with the sugar for 1 minute on low speed. Scrape down the bowl, add the sour cream, and mix on low for another 30 seconds. Scrape the bowl again, boost the speed to medium, and beat until lump-free, 2 to 3 minutes.
With the mixer running, slowly pour in the egg mixture, stopping every now and then to scrape down the bowl. When the mixture is homogenous, pour the filling into the cooled crust.
Line a roasting pan with a kitchen towel. Place the cheesecake to one side of the roasting pan, and pour the boiling water in the other side. Center the cheesecake in the roasting and bake in the oven for 2 hours. Turn the oven off and open the door for 1 minute. Close the door for 1 1/2 hours.
Remove the cheesecake from the water bath and place in the refrigerator for 6 hours to completely cool before serving. Do not attempt to remove the water bath with the cheesecake in it from the oven, unless you like water in your cheesecake.
When ready to serve, place the entire cake pan into a hot water bath for about 15 seconds. Run a small offset spatula around the cheesecake to free the parchment and remove it. Place a piece of wax paper atop the cake and invert a large plate or the bottom of a spring-form pan on top of it. Flip the whole cheesecake over and remove the cake pan. Remove the parchment paper and place a cardboard cake circle or large plate on the bottom of the cake. Flip the whole thing over again and remove the wax paper.
To slice, place your knife (the longest and thinnest blade you’ve got) into a hot water bath and wipe dry each time you make a pass through the cake. Cut into 12 slices.