Preheat oven to 350°F (175°C).
Grease and flour two 9-inch round cake pans; line bottoms with parchment paper.
Whisk flour, baking powder, baking soda, and salt in a bowl; set aside.
Beat butter and sugar until light and fluffy.
Add eggs one at a time, mixing well after each addition.
Mix in vanilla extract.
Gently mix in strawberry puree.
Add dry ingredients in three additions, alternating with milk.
Begin and end with dry ingredients; mix just until combined.
Add food coloring if using.
Divide batter evenly between prepared pans.
Bake for 25–30 minutes until a toothpick inserted comes out clean.
Cool in pans for 10 minutes, then transfer to a wire rack to cool completely.
Beat cream cheese and butter until smooth.
Gradually add powdered sugar and mix well.
Mix in vanilla extract and optional strawberry puree.
Level cake layers if needed.
Spread frosting between layers, then frost top and sides evenly.
Decorate with fresh strawberries if desired.