Preheat oven to 350 degrees Fahrenheit (175 degrees Celsius) and grease a 9x9 inch baking pan.
In a large mixing bowl, combine the strawberry cake mix, eggs, and vegetable oil until a thick, uniform batter forms.
Fold in the white chocolate chips using a spatula.
Transfer the batter to the prepared baking pan and spread evenly to the edges.
Bake for 20 to 25 minutes or until the edges are set and a toothpick inserted into the center comes out mostly clean.
Allow the brownies to cool completely in the pan for approximately 30 minutes.
Whisk together the powdered sugar, milk, and vanilla extract in a small bowl until the glaze reaches a smooth, pourable consistency.
Drizzle the glaze over the cooled brownies and allow it to set before slicing into 12 squares.