Beat butter at medium speed with an electric mixer until creamy; add 1/3 cup sugar, beating well. Gradually add flour, beating at low speed until blended. Stir in 1 teaspoon vanilla and pistachios. Press into bottom and 1 1/2 inches up sides of a 9-inch springform pan.
Bake at 350° for 12 to 15 minutes or until golden. Cool on a wire rack.
Beat cream cheese at medium speed with an electric mixer until light and fluffy; gradually add 1 1/2 cups sugar, beating well. Add eggs, 1 at a time, beating just until yellow disappears. Stir in remaining 2 teaspoons vanilla. (Do not overmix.)
Pour half of batter into crust; sprinkle with chocolate morsels to within 3/4 inch of edge. Pour in remaining batter, starting at outer edge and working toward center. Place cheesecake on a baking sheet.
Bake at 350° for 1 hour or until set. Cool on a wire rack 1 hour. Serve slightly warm with sweetened whipped cream, if desired. Garnish, if desired.