Preheat the Oven: Preheat your oven to 350°F (175°C). Grease and flour a bundt pan to prevent sticking.
Prepare the Cheesecake Filling: In a mixing bowl, beat the softened cream cheese and granulated sugar until smooth. Add the egg and vanilla extract, mixing until fully combined. Fold in the chopped strawberries if desired. Set aside.
Make the Strawberry Cake Batter: In a large bowl, mix the strawberry cake mix, water, vegetable oil, eggs, strawberry puree, and vanilla extract until just combined.
Assemble the Cake: Pour half of the strawberry cake batter into the prepared bundt pan, spreading it evenly. Carefully spoon the cheesecake filling over the batter, avoiding the sides of the pan. Pour the remaining cake batter on top, covering the cheesecake layer completely.
Bake: Place the bundt pan in the preheated oven and bake for 45-50 minutes, or until a toothpick inserted into the cake (avoiding the cheesecake layer) comes out clean.
Cool: Remove the cake from the oven and let it cool in the pan for 10-15 minutes. Then, carefully invert the cake onto a wire rack to cool completely.
Prepare the Glaze: In a small bowl, whisk together powdered sugar, milk, and vanilla extract until smooth. If desired, add pink food coloring for a colorful touch. Adjust the consistency with additional powdered sugar or milk to reach your desired thickness.
Glaze the Cake: Once the cake is completely cooled, drizzle the glaze over the bundt cake and allow it to set for a few minutes.
Serve: Slice and serve your gorgeous Strawberry Cheesecake Bundt Cake!