Mix graham cracker crumbs, butter, and pecans together thoroughly. Press into the bottom of a 10-inch springform pan.
Bake crust in the preheated oven until golden, about 10 minutes. Let cool, about 10 minutes.
Increase oven temperature to 450 degrees F (230 degrees C).
Combine cream cheese, brown sugar, eggs, sour cream, and egg yolks in a large bowl; beat with an electric mixer until smooth. Beat in flour, cinnamon, vanilla extract, nutmeg, allspice, and salt. Fold in sweet potatoes. Blend evaporated milk gradually into the batter.
Pour batter over the cooled crust. Place springform pan in a baking pan. Pour in hot water to a depth of 1 inch.
Bake in the preheated oven until golden, about 15 minutes. Reduce oven temperature to 250 degrees F (120 degrees C). Continue baking until center is firm, about 90 minutes more. Remove pan from the water bath and let cool, at least 1 hour. Chill before serving.