3 vanilla beans
32 ounces cream cheese, thoroughly softened
1 1/4 cups granulated sugar (ideally, use
    Vanilla Sugar; see below)
4 eggs (at room temperature)
1 1/2 cups sour cream
2 1/2 tablespoons vanilla extract (use Tahitian
    vanilla extract, if possible)

Line the bottom of a 9 1/2-inch spring-form pan with foil. Butter the foil and the sides of the pan. Wrap the bottom of the pan in 2 layers of heavy-duty foil.

Preheat the oven to 325 degrees F.

Add the softened cream cheese to the vanilla seed pulp in the large bowl. Beat with an electric mixer at low speed until the cream cheese is creamy and the vanilla is thoroughly distributed. Add the sugar and beat at medium-low speed until everything is thoroughly creamy, scraping down the sides once or twice. If you like your cheesecake especially fluffy, you could beat at medium speed for a couple of minutes at this step, until the mixture just begins to stiffen a little.

Add the eggs, one at a time, beating well at low speed and scraping down the sides after each addition. Beat in the sour cream and vanilla extract, scraping again and beating well until uniform. Scrape the batter into the prepared pan. Place the pan in a large roasting pan or jelly roll pan and pour very, very hot water into the pan around it. (Baking the cheesecake in a water bath helps to keep the edges from drying out and the top from cracking.)

Bake the cheesecake for about one hour. To check it, tap gently on the top at the center; it should jiggle considerably, but not seem liquid.

When this stage is reached, turn off the oven, leave the door just slightly ajar, and leave the cheesecake in the oven for another 45 minutes.

Remove cheesecake from oven, remove it from the water bath, remove the outer layers of foil, and cool on a wire rack until tepid. Refrigerate at least four hours, preferably overnight. Run a thin knife around the outside edge of the cheesecake, remove the side of the spring-form pan, and put a layer of plastic wrap and a cookie sheet on top of the cheesecake. Invert the whole affair, remove the bottom of the pan, and peel off the foil. Place your serving plate on the bottom of the cheesecake, invert again, wrap well in plastic wrap and refrigerate. For optimal flavor and texture, remove the cheesecake from the refrigerator at least one hour before serving.

Vanilla Sugar
Split the vanilla beans lengthwise, and scrape the oily seed pulp into a large mixing bowl. Scrape as much out as you can, but try to avoid getting a lot of the pod lining, as it is fibrous. (A little bit is unavoidable and not really a problem.) Put the scraped-out pods back into the little bottles that they came in, fill bottles with sugar, close them tightly, and set them aside. The next time you make this cheesecake, sift this sugar (which is now vanilla sugar) and use it as the sugar in the recipe for maximal vanilla flavor.