Before getting started on the cake itself, make the strawberry puree & prosecco concentrate.
De-stem the strawberries and blend thoroughly. Set in a saucepan over low heat and allow to cook down for about 30 minutes, until you have ½-⅔ cup remaining. Let the mixture bubble a bit, but stir regularly to prevent burning.
At the same time, make the prosecco concentrate by simmering the prosecco over medium heat. The liquid should take 15-20 minutes to reduce down to 1/3 cup.
Both need to cool completely before using, so it's best to make these the night before baking.
For the strawberry cake:
Preheat the oven to 350°F (175°C). Grease and flour two 9-inch cake pans.
Beat the butter with a mixer on high for 2-3 minutes, until light and fluffy. Add the sugar and beat for another 1-2 minutes, scraping down as needed.
Beat in egg whites for another minute, then add the vanilla and yogurt and beat for another minute.
In a separate bowl, whisk together the flour, salt, baking soda, and baking powder. Add half to the butter mixture, combine at low speed, then add the other. Mix on low until just combined.
On low speed, add ½ cup strawberry puree until just combined.
Divide batter between the two pans and bake for 20-25 minutes. Cakes are done when a toothpick inserted into the center comes out clean. You'll know it's done or nearly done when the cake starts to pull away from the walls of the tin.
Let cakes cool completely before frosting.
Make the prosecco frosting
Beat the butter on high for 3 minutes, until light and fluffy.
Add 1 cup powdered sugar and beat until combined, then add 1 more and repeat.
Add the vanilla, salt and another 1 ½ cups of powdered sugar and beat until combined. Add ¼ cup prosecco concentrate and beat to combine and taste. If you want, add the remaining powdered sugar.
Put it all together
When the cake has cooled completely, cut the tops off both cakes to make sure they're level.
If you have extra strawberry puree, you can always add a layer to the top of the bottom cake layer and swirl with the frosting!
Frost the cake and top with more cut strawberry bits.