I found this recipe in a Jello cookbook. It uses water instead of club soda, but I don't see why you couldn't sub. Also calls for splitting the cake into three layers. Again, you could do it with two and also put the frosting in the hole in the middle. I would think you would use cake mix that does not already have pudding in the mix. I hope this is close to what you remember.

DOUBLE PISTACHIO CAKE DELUXE

1 pkg. (2 layer size) white or yellow cake mix
1 pkg. (4 serving size) Jello instant pistachio pudding mix
4 eggs
1 cup water
1/4 cup vegetable oil
1/4 cup chopped nuts

Combine cake mix, pudding mix, eggs water and oil in large bowl. Beat on low speed of electric mixer just to moisten, scraping sides of bowl often. Beat at medium speed 4 minutes. Stir in nuts. Pour into greased and floured 10 inch bundt pan.

Bake at 350 for 55 minutes or until tester inserted in center comes out clean and cake begins to pull away from sides of pan (do not underbake). Cool in pan 15 minutes. Remove from pan; finish cooling on a rack. Split cake horizontally into three layers.

Fill and frost cake with Fluffy Pistachio Frosting.

FLUFFY PISTACHIO FROSTING

1 cup cold milk
1 pkg. instant pistachio pudding mix
1/4 cup confectioners sugar (optional)
1 (8 oz.) tub of cool whip, thawed

Pour milk into large bowl. Add pudding mix and sugar. Beat with wire whisk until well blended, 1-2 minutes. Fold in Cool Whip. Spread on cooled cake immediately.

Store frosted cake in the refrigerator.