Butter the bottoms and sides of two 9-inch cake pans and dust with flour. Preheat oven to 350 F.
Sift flour, salt and baking powder together into a small bowl. In a separate bowl, mix milk, strawberry puree reduction and vanilla extract. Set both aside.
In a large mixing bowl, or in the bowl of your mixer, place butter and beat on high speed until creamy and light colored. Slowly add sugar and continue to beat until well-integrated and fluffy.
Add eggs, one at a time, beating well after each. Scrape the sides of the bowl with a rubber spatula as you go.
Add dry ingredients and liquids to butter mixture, alternately, beginning and ending with dries.
Divide batter evenly between the two 9-inch cake pans.
Bake for about 20-25 minutes, or until a cake tester comes out clean when inserted into the middle of the cake. Remove from oven and cool for about 5 minutes. Then, turn cakes out of the pans and directly onto a cooling rack. Once cool, refrigerate for about 30 minutes and then slice each layer in half horizontally using a long bread knife or a cake slicing knife. (Chilling the cakes makes slicing them a bit easier.) If the cake layers are significantly domed on top, flatten them out by cutting the rounded part off the top using the same knife.