Preheat oven to 350°F. Prepare crust as directed on package for one-crust pie using 9-inch deep dish pie plate. Beat cream cheese, 1 of the eggs, 1/4 cup of the sugar and 1 teaspoon of the vanilla in large bowl with electric mixer on medium speed until well blended and smooth. Spread evenly on bottom of crust. Bake 15 minutes.
Beat remaining 2 eggs and 1/2 cup sugar with wire whisk in large bowl until very smooth. Add corn syrup, butter, remaining 3 teaspoons vanilla and salt; stir until well blended. Sprinkle walnuts evenly over baked cream cheese layer. Slowly pour corn syrup mixture over nuts.
Bake 35 to 40 minutes or until just set in center. Cool completely on wire rack.