Preheat the oven to 325 degrees.
In the bowl of a stand mixer, combine the cake mix, gelatin, milk, oil, eggs and fresh strawberry puree.
Beat on low speed until mixed, then beat on medium speed for 2 minutes.
Grease and flour two 9" round cake pans (*see instructions below for 9x13 cake pan*).
Divide the batter evenly between the two cake pans.
Bake at 325 degrees for 29 minutes, or until the top of the cake bounces back when you touch it.
Allow the cakes to cool for 10 minutes, then turn them out onto a wire rack to cool completely.
For the Frosting
In the bowl of a stand mixer, cream the softened butter for 1-2 minutes until nearly white in a appearance.
Add 2 cups of powdered sugar and the vanilla extract. Beat on low for 1 minute. Scrape down the sides of the bowl.
Mix in the heavy cream* and another 2 cups of powdered sugar. Beat on low for 1 minute. Scrape down the sides of the bowl.
Add the last 2 cups of powdered sugar and the strawberry jam. Beat on low speed until mixed, then beat on medium speed for 1-2 minutes, until the frosting is creamy and smooth, scraping down the sides as needed.
To Frosting the Cake:
Place one cake layer on a cake plate.
Spread frosting on top of the first layer.
Place the second cake layer on top of the frosting.
Use the remaining frosting to frost the top and sides of the layer cake.
Optional: Decorate the top middle of the cake with a few tablespoons of strawberry jam and fresh strawberries.
Store at room temperature until serving, then store leftovers in the refrigerator.
*Add additional heavy cream by the tablespoon until it is to the consistency you'd like.
**To make a 9x13 cake, prepare the cake as described above. Pour the cake batter in a greased 9x13 cake pan. Bake at 325 degrees for 35 minutes, or until the center of the cake bounces back when you touch it.
***If you make a 9x13 cake, you won't need quite as much frosting. Use these amounts for frosting, preparing it in the same way as described above:1 cup butter, softened4 cups powdered sugar1 teaspoon vanilla extract4-5 tablespoons heavy cream1/3 cup strawberry jam