Thick brush a 9-inch springform pan with half of the melted butter and place in the freezer to harden, about 10 minutes. When hard, repeat to make a thick coating of butter.
Adjust your oven rack to the lowest position and heat the oven to 350 degrees F.
Beat the cream cheese in a mixer fitted with a paddle attachment (or using a hand mixer) until fluffy and very smooth. Beat in the extracts, nutmeg, sugar, and salt. Add the eggs one at a time, scraping down the bowl after each addition. Pour into pan. Place the pan on a double-layer sheet of aluminum foil, with at least 3 inches of foil all around pan.
Fill a roasting pan large enough to hold the cake pan with hot water to a depth of about 1-inch, then lift the foil wrapped cake into the roasting pan, keeping the foil turned up so that it prevents water from overflowing or seeping into the cake. The foil should not be closed over the top of the cake. Be careful not to tear any holes in the foil.
Bake until the top of the cake is golden brown and dry to the touch, though still a bit soft in the center, about 1 1/2 hours. It should "shimmy" a bit when you shake the pan; it will firm up more as it cools.
Remove the pan from the water bath, remove the foil, and let cool at room temperature 15 minutes. Refrigerate, uncovered, 2 hours before removing the cake from the pan.
To remove the cake from the pan, first remove the sides. Cover the surface the with plastic wrap. Place a large plate over the cake, then flip the cake over onto the plate, tapping if necessary to help the cake come away from the pan bottom. If tapping doesn't do the trick, try a blow torch or stove burner to warm the bottom of the pan to loosen it.
Remove the pan bottom and evenly sprinkle the exposed surface with graham cracker crumbs. Place a serving plate over the crumbs and flip the cake again so that the crumbs form the bottom crust and the top is covered with plastic. Refrigerate, lightly covered, at least 3 hours or overnight before serving.
Recipe courtesy of Gale Gand, "Butter Sugar Flour Eggs" by Gale Gand, Rick Tramonto, Julia Moskin: Clarkson N. Potter Publishers, 1999