Preheat oven to 350°F (175°C) and generously grease and flour a 10-inch bundt pan.
Whisk together flour, baking powder, baking soda, and salt in a medium bowl.
Cream the butter and granulated sugar in a large bowl until light and fluffy, approximately 5 minutes.
Incorporate eggs one at a time, beating well after each addition, then stir in the vanilla extract.
Whisk together the 1/2 cup strawberry puree, sour cream, and milk in a separate small bowl.
Add the dry ingredients to the butter mixture in three parts, alternating with the strawberry-liquid mixture, starting and ending with the dry ingredients.
Transfer the batter to the prepared bundt pan and smooth the surface with a spatula.
Bake for 50 to 60 minutes or until a skewer inserted into the center comes out clean.
Cool the cake in the pan for 15 minutes before inverting onto a wire rack to cool completely.
Whisk powdered sugar and remaining strawberry puree until smooth; drizzle over the cooled cake before serving.