Preheat oven to 350. Grease two 9 inch round cake pans with solid vegetable shortening, then dust with flour. Shake out excess flour.
Place about 8 of the peach halves in a food processor fitted with the steel blad and process until smooth. This should measure about 1 1/2 cups. Reserve 1/2 cup syrup and the remaining peach halves.
Place cake mix, peach puree, melted butter, eggs, and vanilla in mixing bowl. Blend with mixer on low, for 1 minute. Stop the machine and scrape down sides of bowl. Increase mixer speed to medium, and beat 2 to 3 minutes more, scraping down sides again if needed. Divide batter between prepared pans. Place in the oven.
Bake cakes until golden brown and spring back when lightly pressed with your finger, 28-32 minutes. Remove pans from oven and cool on wire rack 10 minutes. Run a dinner knife around the edge of each layer and invert each onto a rack. While layers are still warm, poke holes in top of them with toothpick or wooden skewer. Carefully pour reserved peach syrup over the layers so that the cake soaks up all the juice. Let the layers cool completely.
Meanwhile, prepare sweetened cream and served in the refrigerator. (Instructions for sweetened cream at bottom.) Cut the remaining peach halves into 1/2 inch thick slices. Place one cake layer, right side up, on serving platter. Spread the top with sweetened cream. Place the second layer, right side up, on top of the first and frost the top and sides of the cake with clean, smooth strokes. Arrange the peach slices attractively on top of the cake.
Place a clean, large mixing bowl and electric mixer beaters in the freezer for a few minutes while you assemble the ingredients. Pour the whipping cream into the chilled bowl and beat with the electric mixer on high speed until the cream has thickened, 1 1/2 minutes. Stop the machine and add the sugar. Beat the cream and sugar on high speed until stiff peaks form, 1 to 2 minutes.